module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 1086,
"column": 2
} | {
"line": 1086,
"column": 30
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁴ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\ns : Set M\nF' : Type u_21\ninst✝¹ : N... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 1091,
"column": 2
} | {
"line": 1091,
"column": 30
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁴ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\nF' : Type u_21\ninst✝¹ : NormedDivisi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 1115,
"column": 2
} | {
"line": 1115,
"column": 40
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁴ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\ns : Set M\nz : M\nF' : Type u_21\nins... | convert! hp.mul (hq.inv hq_ne) using 1 | Mathlib.Tactic._aux_Mathlib_Tactic_Convert___macroRules_Mathlib_Tactic_convert!_1 | Mathlib.Tactic.convert! |
Mathlib.Topology.VectorBundle.Hom | {
"line": 110,
"column": 4
} | {
"line": 114,
"column": 19
} | [
{
"pp": "𝕜₁ : Type u_1\ninst✝²⁰ : NontriviallyNormedField 𝕜₁\n𝕜₂ : Type u_2\ninst✝¹⁹ : NontriviallyNormedField 𝕜₂\nσ : 𝕜₁ →+* 𝕜₂\nB : Type u_3\nF₁ : Type u_4\ninst✝¹⁸ : NormedAddCommGroup F₁\ninst✝¹⁷ : NormedSpace 𝕜₁ F₁\nE₁ : B → Type u_5\ninst✝¹⁶ : (x : B) → AddCommGroup (E₁ x)\ninst✝¹⁵ : (x : B) → Modu... | simp only [Prod.mk_right_inj]
ext v
dsimp only [comp_apply]
rw [Trivialization.continuousLinearMapAt_symmL, Trivialization.continuousLinearMapAt_symmL]
exacts [h₁, h₂] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.VectorBundle.Hom | {
"line": 110,
"column": 4
} | {
"line": 114,
"column": 19
} | [
{
"pp": "𝕜₁ : Type u_1\ninst✝²⁰ : NontriviallyNormedField 𝕜₁\n𝕜₂ : Type u_2\ninst✝¹⁹ : NontriviallyNormedField 𝕜₂\nσ : 𝕜₁ →+* 𝕜₂\nB : Type u_3\nF₁ : Type u_4\ninst✝¹⁸ : NormedAddCommGroup F₁\ninst✝¹⁷ : NormedSpace 𝕜₁ F₁\nE₁ : B → Type u_5\ninst✝¹⁶ : (x : B) → AddCommGroup (E₁ x)\ninst✝¹⁵ : (x : B) → Modu... | simp only [Prod.mk_right_inj]
ext v
dsimp only [comp_apply]
rw [Trivialization.continuousLinearMapAt_symmL, Trivialization.continuousLinearMapAt_symmL]
exacts [h₁, h₂] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Manifold.MFDeriv.NormedSpace | {
"line": 98,
"column": 2
} | {
"line": 98,
"column": 34
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁴ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\ns : Set M\nx : M\nF : Type u_18\ninst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.NormedSpace | {
"line": 106,
"column": 2
} | {
"line": 106,
"column": 34
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁵ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁴ : TopologicalSpace M\ninst✝³ : ChartedSpace H M\ns : Set M\nx : M\nF : Type u_18\ninst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.NormedSpace | {
"line": 290,
"column": 4
} | {
"line": 290,
"column": 15
} | [
{
"pp": "case right\n𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁴ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\nx : M\nV : Type u_18\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.NormedSpace | {
"line": 381,
"column": 2
} | {
"line": 381,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁴ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\nx : M\nV : Type u_18\ninst✝¹ : Normed... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.NormedSpace | {
"line": 503,
"column": 2
} | {
"line": 503,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁴ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\nF : Type u_8\ninst✝¹ : NormedAddCommG... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.Hom | {
"line": 197,
"column": 6
} | {
"line": 197,
"column": 29
} | [
{
"pp": "case h\n𝕜 : Type u_1\nF₁ : Type u_2\nF₂ : Type u_3\nB₁ : Type u_4\nB₂ : Type u_5\nM : Type u_6\nE₁ : B₁ → Type u_7\nE₂ : B₂ → Type u_8\ninst✝³¹ : NontriviallyNormedField 𝕜\ninst✝³⁰ : (x : B₁) → AddCommGroup (E₁ x)\ninst✝²⁹ : (x : B₁) → Module 𝕜 (E₁ x)\ninst✝²⁸ : NormedAddCommGroup F₁\ninst✝²⁷ : Norm... | inCoordinates_eq hm h'm | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Manifold.VectorField.Pullback | {
"line": 349,
"column": 2
} | {
"line": 349,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹³ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝¹² : TopologicalSpace H\nE : Type u_3\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁹ : TopologicalSpace M\ninst✝⁸ : ChartedSpace H M\nH' : Type u_5\ninst✝⁷ : Topologic... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 115,
"column": 4
} | {
"line": 115,
"column": 19
} | [
{
"pp": "case hV\n𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝⁴ : TopologicalSpace H\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\ns : Set M\nx : M\nV W : (x : ... | simp +instances | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Geometry.Manifold.VectorField.Pullback | {
"line": 376,
"column": 2
} | {
"line": 376,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹³ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝¹² : TopologicalSpace H\nE : Type u_3\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁹ : TopologicalSpace M\ninst✝⁸ : ChartedSpace H M\nH' : Type u_5\ninst✝⁷ : Topologic... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 119,
"column": 4
} | {
"line": 119,
"column": 19
} | [
{
"pp": "case hW\n𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝⁴ : TopologicalSpace H\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\ns : Set M\nx : M\nV W : (x : ... | simp +instances | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Geometry.Manifold.VectorField.Pullback | {
"line": 558,
"column": 2
} | {
"line": 558,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹³ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝¹² : TopologicalSpace H\nE : Type u_3\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁹ : TopologicalSpace M\ninst✝⁸ : ChartedSpace H M\nH' : Type u_5\ninst✝⁷ : Topologic... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorField.Pullback | {
"line": 607,
"column": 2
} | {
"line": 607,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹³ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝¹² : TopologicalSpace H\nE : Type u_3\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁹ : TopologicalSpace M\ninst✝⁸ : ChartedSpace H M\nH' : Type u_5\ninst✝⁷ : Topologic... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 385,
"column": 4
} | {
"line": 385,
"column": 24
} | [
{
"pp": "case e_a\n𝕜 : 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\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\ns : Set M\nx : M\nV W : (x ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.ContMDiffMFDeriv | {
"line": 168,
"column": 43
} | {
"line": 168,
"column": 54
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁵ : NontriviallyNormedField 𝕜\nm n : WithTop ℕ∞\nE : Type u_2\ninst✝¹⁴ : NormedAddCommGroup E\ninst✝¹³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹¹ : TopologicalSpace M\ninst✝¹⁰ : ChartedSpace H M\nE' : Type u_5... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.LocalSourceTargetProperty | {
"line": 184,
"column": 4
} | {
"line": 184,
"column": 15
} | [
{
"pp": "case refine_1\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_4\nH : Type u_6\nG : Type u_8\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\ninst✝⁵ : TopologicalSpace H\ninst✝⁴ : TopologicalSpace G\nI : M... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 427,
"column": 2
} | {
"line": 427,
"column": 35
} | [
{
"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\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\ns : Set M\nx : M\nV W : (x : M) → Tan... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 438,
"column": 2
} | {
"line": 438,
"column": 35
} | [
{
"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\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\ns : Set M\nx : M\nV W : (x : M) → Tan... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.ContMDiffMFDeriv | {
"line": 172,
"column": 4
} | {
"line": 174,
"column": 62
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁵ : NontriviallyNormedField 𝕜\nm n : WithTop ℕ∞\nE : Type u_2\ninst✝¹⁴ : NormedAddCommGroup E\ninst✝¹³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹¹ : TopologicalSpace M\ninst✝¹⁰ : ChartedSpace H M\nE' : Type u_5... | · apply (mdifferentiableWithinAt_extChartAt_symm _).mono
· exact inter_subset_left.trans (extChartAt_target_subset_range (g x₀))
· exact PartialEquiv.map_source (extChartAt I (g x₀)) h2 | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 582,
"column": 80
} | {
"line": 582,
"column": 91
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁴ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝¹³ : TopologicalSpace H\nE : Type u_3\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹⁰ : TopologicalSpace M\ninst✝⁹ : ChartedSpace H M\nH' : Type u_5\ninst✝⁸ : Topologi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 592,
"column": 6
} | {
"line": 592,
"column": 83
} | [
{
"pp": "case h.hf\n𝕜 : Type u_1\ninst✝¹⁴ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝¹³ : TopologicalSpace H\nE : Type u_3\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹⁰ : TopologicalSpace M\ninst✝⁹ : ChartedSpace H M\nH' : Type u_5\ninst✝⁸... | exact (mdifferentiableWithinAt_extChartAt_symm h'''y).mono inter_subset_right | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 592,
"column": 6
} | {
"line": 592,
"column": 83
} | [
{
"pp": "case h.hf\n𝕜 : Type u_1\ninst✝¹⁴ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝¹³ : TopologicalSpace H\nE : Type u_3\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹⁰ : TopologicalSpace M\ninst✝⁹ : ChartedSpace H M\nH' : Type u_5\ninst✝⁸... | exact (mdifferentiableWithinAt_extChartAt_symm h'''y).mono inter_subset_right | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 592,
"column": 6
} | {
"line": 592,
"column": 83
} | [
{
"pp": "case h.hf\n𝕜 : Type u_1\ninst✝¹⁴ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝¹³ : TopologicalSpace H\nE : Type u_3\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹⁰ : TopologicalSpace M\ninst✝⁹ : ChartedSpace H M\nH' : Type u_5\ninst✝⁸... | exact (mdifferentiableWithinAt_extChartAt_symm h'''y).mono inter_subset_right | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Manifold.ContMDiffMFDeriv | {
"line": 184,
"column": 4
} | {
"line": 184,
"column": 15
} | [
{
"pp": "case h.hx\n𝕜 : Type u_1\ninst✝¹⁵ : NontriviallyNormedField 𝕜\nm n : WithTop ℕ∞\nE : Type u_2\ninst✝¹⁴ : NormedAddCommGroup E\ninst✝¹³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹¹ : TopologicalSpace M\ninst✝¹⁰ : ChartedSpace H M\nE'... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.ContMDiffMFDeriv | {
"line": 184,
"column": 4
} | {
"line": 184,
"column": 18
} | [
{
"pp": "case h.hx\n𝕜 : Type u_1\ninst✝¹⁵ : NontriviallyNormedField 𝕜\nm n : WithTop ℕ∞\nE : Type u_2\ninst✝¹⁴ : NormedAddCommGroup E\ninst✝¹³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹¹ : TopologicalSpace M\ninst✝¹⁰ : ChartedSpace H M\nE'... | simpa using h2 | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Geometry.Manifold.ContMDiffMFDeriv | {
"line": 184,
"column": 4
} | {
"line": 184,
"column": 18
} | [
{
"pp": "case h.hx\n𝕜 : Type u_1\ninst✝¹⁵ : NontriviallyNormedField 𝕜\nm n : WithTop ℕ∞\nE : Type u_2\ninst✝¹⁴ : NormedAddCommGroup E\ninst✝¹³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹¹ : TopologicalSpace M\ninst✝¹⁰ : ChartedSpace H M\nE'... | simpa using h2 | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Manifold.ContMDiffMFDeriv | {
"line": 184,
"column": 4
} | {
"line": 184,
"column": 18
} | [
{
"pp": "case h.hx\n𝕜 : Type u_1\ninst✝¹⁵ : NontriviallyNormedField 𝕜\nm n : WithTop ℕ∞\nE : Type u_2\ninst✝¹⁴ : NormedAddCommGroup E\ninst✝¹³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹¹ : TopologicalSpace M\ninst✝¹⁰ : ChartedSpace H M\nE'... | simpa using h2 | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Manifold.ContMDiffMFDeriv | {
"line": 185,
"column": 4
} | {
"line": 185,
"column": 15
} | [
{
"pp": "case h.hy\n𝕜 : Type u_1\ninst✝¹⁵ : NontriviallyNormedField 𝕜\nm n : WithTop ℕ∞\nE : Type u_2\ninst✝¹⁴ : NormedAddCommGroup E\ninst✝¹³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹¹ : TopologicalSpace M\ninst✝¹⁰ : ChartedSpace H M\nE'... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Instances.Real | {
"line": 150,
"column": 2
} | {
"line": 150,
"column": 51
} | [
{
"pp": "case h\nn : ℕ\np : ℝ≥0∞\na : ℝ\ni : Fin n\ny : PiLp p fun x ↦ ℝ\n⊢ y ∈ {y | a ≤ y.ofLp i} \\ {y | a < y.ofLp i} ↔ y ∈ {y | a = y.ofLp i}",
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Real",
"congrArg",
"PartialOrder.toPreorder",
"setOf",
"Real.instLT",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.ContMDiffMFDeriv | {
"line": 198,
"column": 2
} | {
"line": 198,
"column": 71
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nm n : WithTop ℕ∞\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\nins... | exact this.mfderivWithin contMDiffWithinAt_id hx (mapsTo_id _) hmn hs | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Geometry.Manifold.ContMDiffMFDeriv | {
"line": 310,
"column": 2
} | {
"line": 310,
"column": 33
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nm n : WithTop ℕ∞\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\nins... | rw [← contMDiffOn_univ] at hf ⊢ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Manifold.Immersion | {
"line": 359,
"column": 2
} | {
"line": 359,
"column": 81
} | [
{
"pp": "case h\n𝕜 : Type u_1\ninst✝²⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\nE' : Type u_3\nE''' : Type u_4\nE'' : Type u\nF : Type u_5\nF' : Type u_6\ninst✝²⁷ : NormedAddCommGroup E\ninst✝²⁶ : NormedSpace 𝕜 E\ninst✝²⁵ : NormedAddCommGroup E'\ninst✝²⁴ : NormedSpace 𝕜 E'\ninst✝²³ : NormedAddCommGroup E'... | rw [φ₁.extend_prod φ₂, ψ₁.extend_prod, PartialEquiv.prod_target, eqOn_prod_iff] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Manifold.Immersion | {
"line": 360,
"column": 30
} | {
"line": 360,
"column": 41
} | [
{
"pp": "𝕜 : Type u_1\ninst✝²⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\nE' : Type u_3\nE''' : Type u_4\nE'' : Type u\nF : Type u_5\nF' : Type u_6\ninst✝²⁷ : NormedAddCommGroup E\ninst✝²⁶ : NormedSpace 𝕜 E\ninst✝²⁵ : NormedAddCommGroup E'\ninst✝²⁴ : NormedSpace 𝕜 E'\ninst✝²³ : NormedAddCommGroup E''\ninst✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Immersion | {
"line": 360,
"column": 74
} | {
"line": 360,
"column": 85
} | [
{
"pp": "𝕜 : Type u_1\ninst✝²⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\nE' : Type u_3\nE''' : Type u_4\nE'' : Type u\nF : Type u_5\nF' : Type u_6\ninst✝²⁷ : NormedAddCommGroup E\ninst✝²⁶ : NormedSpace 𝕜 E\ninst✝²⁵ : NormedAddCommGroup E'\ninst✝²⁴ : NormedSpace 𝕜 E'\ninst✝²³ : NormedAddCommGroup E''\ninst✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Instances.Real | {
"line": 392,
"column": 6
} | {
"line": 392,
"column": 31
} | [
{
"pp": "case neg\nx✝ y✝ : ℝ\nhxy : Fact (x✝ < y✝)\nx y : ℝ\nh : Fact (x < y)\nz : ↑(Icc x y)\nh' : ¬↑z < y\n⊢ y ≤ ↑z",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Instances.Real | {
"line": 433,
"column": 6
} | {
"line": 433,
"column": 68
} | [
{
"pp": "case h.inr.inr.ha\nx y : ℝ\nhxy : Fact (x < y)\np : ↑(Icc x y)\nhp : ↑p ∈ Ioo x y\n⊢ p ∉ ModelWithCorners.boundary ↑(Icc x y)",
"usedConstants": [
"ModelWithCorners.compl_boundary",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Re... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 624,
"column": 2
} | {
"line": 624,
"column": 15
} | [
{
"pp": "case hf\n𝕜 : Type u_1\ninst✝¹⁴ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝¹³ : TopologicalSpace H\nE : Type u_3\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹⁰ : TopologicalSpace M\ninst✝⁹ : ChartedSpace H M\nH' : Type u_5\ninst✝⁸ :... | · exact hsymm | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Geometry.Manifold.Instances.Icc | {
"line": 86,
"column": 6
} | {
"line": 86,
"column": 17
} | [
{
"pp": "case pos.hx\nx y : ℝ\nh : Fact (x < y)\nn : WithTop ℕ∞\nz : ↑(Icc x y)\nhz : ↑z < y\nthis : ContDiff ℝ n fun z ↦ z.ofLp 0 + x\n⊢ (toLp 2 fun x_1 ↦ ↑z - x) ∈ {x | 0 ≤ x.ofLp 0}",
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Real",
"Real.instZero",
"Real.instSub",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Instances.Icc | {
"line": 89,
"column": 6
} | {
"line": 89,
"column": 17
} | [
{
"pp": "x y : ℝ\nh : Fact (x < y)\nn : WithTop ℕ∞\nz : ↑(Icc x y)\nhz : ↑z < y\nthis : ContDiff ℝ n fun z ↦ z.ofLp 0 + x\n⊢ (toLp 2 fun i ↦ ↑z - x) ∈ {b | b.ofLp 0 < y - x}",
"usedConstants": [
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"Eq.mpr",
"Real.partialOrder",
"Re... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Instances.Icc | {
"line": 102,
"column": 6
} | {
"line": 102,
"column": 17
} | [
{
"pp": "case neg.hx\nx y : ℝ\nh : Fact (x < y)\nn : WithTop ℕ∞\nz : ↑(Icc x y)\nhz : y ≤ ↑z\nthis : ContDiff ℝ n fun z ↦ y - z.ofLp 0\n⊢ (toLp 2 fun x_1 ↦ y - ↑z) ∈ {x | 0 ≤ x.ofLp 0}",
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Real",
"Real.instZero",
"Real.instSub",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Instances.Icc | {
"line": 105,
"column": 6
} | {
"line": 105,
"column": 17
} | [
{
"pp": "x y : ℝ\nh : Fact (x < y)\nn : WithTop ℕ∞\nz : ↑(Icc x y)\nhz : y ≤ ↑z\nthis : ContDiff ℝ n fun z ↦ y - z.ofLp 0\n⊢ (toLp 2 fun i ↦ y - ↑z) ∈ {b | b.ofLp 0 < y - x}",
"usedConstants": [
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"Eq.mpr",
"Real.partialOrder",
"Re... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 630,
"column": 6
} | {
"line": 631,
"column": 26
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁴ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝¹³ : TopologicalSpace H\nE : Type u_3\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹⁰ : TopologicalSpace M\ninst✝⁹ : ChartedSpace H M\nH' : Type u_5\ninst✝⁸ : Topologi... | exact (contMDiffWithinAt_extChartAt_symm_range _ (mem_extChartAt_target x₀)).mono
inter_subset_right | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 630,
"column": 6
} | {
"line": 631,
"column": 26
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁴ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝¹³ : TopologicalSpace H\nE : Type u_3\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹⁰ : TopologicalSpace M\ninst✝⁹ : ChartedSpace H M\nH' : Type u_5\ninst✝⁸ : Topologi... | exact (contMDiffWithinAt_extChartAt_symm_range _ (mem_extChartAt_target x₀)).mono
inter_subset_right | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 630,
"column": 6
} | {
"line": 631,
"column": 26
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁴ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝¹³ : TopologicalSpace H\nE : Type u_3\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹⁰ : TopologicalSpace M\ninst✝⁹ : ChartedSpace H M\nH' : Type u_5\ninst✝⁸ : Topologi... | exact (contMDiffWithinAt_extChartAt_symm_range _ (mem_extChartAt_target x₀)).mono
inter_subset_right | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Manifold.Instances.Icc | {
"line": 162,
"column": 2
} | {
"line": 162,
"column": 35
} | [
{
"pp": "E : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\nH : Type u_2\ninst✝² : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\nx y : ℝ\nh : Fact (x < y)\nf : ↑(Icc x y) → M\nw : ↑(Icc x y)\n⊢ MDiffAt[Icc x y] (f ∘ projI... | refine ⟨fun hf ↦ ?_, fun hf ↦ ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Geometry.Manifold.IntegralCurve.Transform | {
"line": 44,
"column": 18
} | {
"line": 44,
"column": 98
} | [
{
"pp": "E : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\nH : Type u_2\ninst✝² : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\nγ : ℝ → M\nv : (x : M) → TangentSpace I x\ns : Set ℝ\nhγ : IsMIntegralCurveOn γ v s\ndt t : ... | ← ContinuousLinearMap.comp_id (ContinuousLinearMap.smulRight 1 (v (γ (t + dt)))) | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Manifold.IntegralCurve.Transform | {
"line": 60,
"column": 2
} | {
"line": 60,
"column": 13
} | [
{
"pp": "E : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\nH : Type u_2\ninst✝² : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\nγ : ℝ → M\nv : (x : M) → TangentSpace I x\ns : Set ℝ\ndt : ℝ\n⊢ IsMIntegralCurveOn (γ ∘ fun ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IntegralCurve.Transform | {
"line": 81,
"column": 2
} | {
"line": 81,
"column": 13
} | [
{
"pp": "E : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\nH : Type u_2\ninst✝² : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\nγ : ℝ → M\nv : (x : M) → TangentSpace I x\nt₀ dt : ℝ\n⊢ IsMIntegralCurveAt (γ ∘ fun x ↦ x - ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IntegralCurve.Transform | {
"line": 86,
"column": 2
} | {
"line": 86,
"column": 13
} | [
{
"pp": "E : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\nH : Type u_2\ninst✝² : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\nγ : ℝ → M\nv : (x : M) → TangentSpace I x\nhγ : IsMIntegralCurveOn γ v univ\ndt : ℝ\n⊢ IsMIn... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Instances.Sphere | {
"line": 134,
"column": 4
} | {
"line": 134,
"column": 71
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : InnerProductSpace ℝ E\nv : E\nhv : ‖v‖ = 1\nw : E\nhw : w ∈ (ℝ ∙ v)ᗮ\nh₁ : 0 < ‖w‖ ^ 2 + 4\nthis : ‖4 • w + (‖w‖ ^ 2 - 4) • v‖ ^ 2 = (‖w‖ ^ 2 + 4) ^ 2\n⊢ ‖4 • w + (‖w‖ ^ 2 - 4) • v‖ = ‖w‖ ^ 2 + 4",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IntegralCurve.Transform | {
"line": 97,
"column": 2
} | {
"line": 97,
"column": 13
} | [
{
"pp": "E : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\nH : Type u_2\ninst✝² : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\nγ : ℝ → M\nv : (x : M) → TangentSpace I x\ndt : ℝ\n⊢ IsMIntegralCurve (γ ∘ fun x ↦ x - dt) v... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Instances.Sphere | {
"line": 146,
"column": 4
} | {
"line": 146,
"column": 81
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : InnerProductSpace ℝ E\nv : E\nh₀ : HasFDerivAt (fun w ↦ ‖w‖ ^ 2) 0 0\n⊢ HasFDerivAt (fun w ↦ (‖w‖ ^ 2 + 4)⁻¹) 0 0",
"usedConstants": [
"ContinuousLinearMap.comp",
"HasFDerivAt",
"NormedCommRing.toNormedRing",
"Norm.norm",
... | convert! (hasFDerivAt_inv _).comp _ (h₀.add (hasFDerivAt_const 4 0)) <;> simp | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Geometry.Manifold.Instances.Sphere | {
"line": 195,
"column": 4
} | {
"line": 196,
"column": 15
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : InnerProductSpace ℝ E\nv : E\nhv : ‖v‖ = 1\nw : ↥(ℝ ∙ v)ᗮ\nhw : ⟪v, ↑w⟫_ℝ = 0\nhw' : (‖↑w‖ ^ 2 + 4)⁻¹ * (‖↑w‖ ^ 2 - 4) < 1\n⊢ ⟪↑(stereoInvFun hv w), v⟫_ℝ < 1",
"usedConstants": [
"one_pow",
"Norm.norm",
"Eq.mpr",
"InnerPro... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Instances.Sphere | {
"line": 197,
"column": 4
} | {
"line": 197,
"column": 15
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : InnerProductSpace ℝ E\nv : E\nhv : ‖v‖ = 1\nw : ↥(ℝ ∙ v)ᗮ\n⊢ ‖↑(stereoInvFun hv w)‖ = 1",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Submodule",
"Real",
"instHSMul",
"Re... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IntegralCurve.Basic | {
"line": 125,
"column": 4
} | {
"line": 125,
"column": 53
} | [
{
"pp": "E : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\nH : Type u_2\ninst✝² : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\nγ : ℝ → M\nv : (x : M) → TangentSpace I x\nh✝ : ∀ (t : ℝ), IsMIntegralCurveAt γ v t\nt : ℝ\n... | exact h t (mem_of_mem_nhds hs) |>.hasMFDerivAt hs | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Geometry.Manifold.Instances.Sphere | {
"line": 222,
"column": 4
} | {
"line": 222,
"column": 16
} | [
{
"pp": "case h.e'_3.h.e'_6\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : InnerProductSpace ℝ E\nv : E\nhv : ‖v‖ = 1\nx : ↑(sphere 0 1)\nhx : ↑x ≠ v\na : ℝ := ((innerSL ℝ) v) ↑x\ny : ↥(ℝ ∙ v)ᗮ := (ℝ ∙ v)ᗮ.orthogonalProjection ↑x\nsplit : ↑x = a • v + ↑y\nhvy : ⟪v, ↑y⟫_ℝ = 0\nhvy' : ⟪a • v, ↑y⟫_ℝ = 0\n⊢ ... | · exact sq _ | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 684,
"column": 4
} | {
"line": 685,
"column": 38
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹³ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝¹² : TopologicalSpace H\nE : Type u_3\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁹ : TopologicalSpace M\ninst✝⁸ : ChartedSpace H M\nH' : Type u_5\ninst✝⁷ : Topologic... | obtain ⟨u, u_open, x₀u, hu⟩ : ∃ u, IsOpen u ∧ x₀ ∈ u ∧ CMDiff[insert x₀ s ∩ u] 2 f :=
hf.contMDiffOn' le_rfl (by simp) | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Geometry.Manifold.Instances.Sphere | {
"line": 230,
"column": 2
} | {
"line": 231,
"column": 33
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : InnerProductSpace ℝ E\nv : E\nhv : ‖v‖ = 1\nx : ↑(sphere 0 1)\nhx : ↑x ≠ v\na : ℝ := ((innerSL ℝ) v) ↑x\ny : ↥(ℝ ∙ v)ᗮ := (ℝ ∙ v)ᗮ.orthogonalProjection ↑x\nsplit : ↑x = a • v + ↑y\nhvy : ⟪v, ↑y⟫_ℝ = 0\npythag : 1 = a ^ 2 + ‖y‖ ^ 2\nha : 0 < 1 - a\n⊢ ... | · field_simp
linear_combination 4 * pythag | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Geometry.Manifold.Instances.Sphere | {
"line": 236,
"column": 2
} | {
"line": 237,
"column": 77
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : InnerProductSpace ℝ E\nv : E\nhv : ‖v‖ = 1\nw : ↥(ℝ ∙ v)ᗮ\n⊢ stereoToFun v ↑(stereoInvFun hv w) = w",
"usedConstants": [
"NormedCommRing.toNormedRing",
"Norm.norm",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Norme... | simp only [stereoToFun, stereoInvFun, stereoInvFunAux, smul_add, map_add, map_smul,
innerSL_apply_apply, Submodule.orthogonalProjection_mem_subspace_eq_self] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Geometry.Manifold.Instances.Sphere | {
"line": 357,
"column": 27
} | {
"line": 357,
"column": 38
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\nn : ℕ\ninst✝ : Fact (finrank ℝ E = n + 1)\nv : ↑(sphere 0 1)\n⊢ v ∈ (stereographic' n (-v)).source",
"usedConstants": [
"stereographic'",
"Eq.mpr",
"Real",
"stereographic'_source",
"congrArg",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 716,
"column": 32
} | {
"line": 716,
"column": 43
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹³ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝¹² : TopologicalSpace H\nE : Type u_3\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁹ : TopologicalSpace M\ninst✝⁸ : ChartedSpace H M\nH' : Type u_5\ninst✝⁷ : Topologic... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Instances.Sphere | {
"line": 459,
"column": 31
} | {
"line": 459,
"column": 42
} | [
{
"pp": "E : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : InnerProductSpace ℝ E\nm : ℕ∞ω\nF : Type u_2\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace ℝ F\nH : Type u_3\ninst✝⁴ : TopologicalSpace H\nI : ModelWithCorners ℝ F H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\ninst✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Instances.Sphere | {
"line": 539,
"column": 2
} | {
"line": 539,
"column": 38
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\nn : ℕ\ninst✝ : Fact (finrank ℝ E = n + 1)\nv : ↑(sphere 0 1)\nU : ↥(ℝ ∙ ↑(-v))ᗮ ≃ₗᵢ[ℝ] EuclideanSpace ℝ (Fin n) := (OrthonormalBasis.fromOrthogonalSpanSingleton n ⋯).repr\nthis✝ : HasFDerivAt (stereoInvFunAux (-↑v) ∘ Subtype.v... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Riemannian.PathELength | {
"line": 70,
"column": 67
} | {
"line": 70,
"column": 85
} | [
{
"pp": "E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\nH : Type u_2\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\ninst✝ : (x : M) → ENorm (TangentSpace I x)\na b : ℝ\nγ : ℝ → M\n⊢ pathELength I γ a b = ∫⁻ ... | simp [pathELength] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Geometry.Manifold.Riemannian.PathELength | {
"line": 70,
"column": 67
} | {
"line": 70,
"column": 85
} | [
{
"pp": "E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\nH : Type u_2\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\ninst✝ : (x : M) → ENorm (TangentSpace I x)\na b : ℝ\nγ : ℝ → M\n⊢ pathELength I γ a b = ∫⁻ ... | simp [pathELength] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Manifold.Riemannian.PathELength | {
"line": 70,
"column": 67
} | {
"line": 70,
"column": 85
} | [
{
"pp": "E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\nH : Type u_2\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\ninst✝ : (x : M) → ENorm (TangentSpace I x)\na b : ℝ\nγ : ℝ → M\n⊢ pathELength I γ a b = ∫⁻ ... | simp [pathELength] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Manifold.Riemannian.PathELength | {
"line": 86,
"column": 2
} | {
"line": 86,
"column": 20
} | [
{
"pp": "E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\nH : Type u_2\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\ninst✝ : (x : M) → ENorm (TangentSpace I x)\na : ℝ\nγ : ℝ → M\n⊢ pathELength I γ a a = 0",
... | simp [pathELength] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Geometry.Manifold.Riemannian.PathELength | {
"line": 86,
"column": 2
} | {
"line": 86,
"column": 20
} | [
{
"pp": "E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\nH : Type u_2\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\ninst✝ : (x : M) → ENorm (TangentSpace I x)\na : ℝ\nγ : ℝ → M\n⊢ pathELength I γ a a = 0",
... | simp [pathELength] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Manifold.Riemannian.PathELength | {
"line": 86,
"column": 2
} | {
"line": 86,
"column": 20
} | [
{
"pp": "E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\nH : Type u_2\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\ninst✝ : (x : M) → ENorm (TangentSpace I x)\na : ℝ\nγ : ℝ → M\n⊢ pathELength I γ a a = 0",
... | simp [pathELength] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Manifold.Riemannian.PathELength | {
"line": 103,
"column": 2
} | {
"line": 103,
"column": 52
} | [
{
"pp": "E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\nH : Type u_2\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\ninst✝ : (x : M) → ENorm (TangentSpace I x)\na b a' b' : ℝ\nγ : ℝ → M\nh : a' ≤ a\nh' : b ≤ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 855,
"column": 9
} | {
"line": 855,
"column": 71
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝⁷ : TopologicalSpace H\nE : Type u_3\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁴ : TopologicalSpace M\ninst✝³ : ChartedSpace H M\ninst✝² : IsManifold I (minSmoothness ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Riemannian.PathELength | {
"line": 233,
"column": 26
} | {
"line": 233,
"column": 45
} | [
{
"pp": "E : Type u_1\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\nH : Type u_2\ninst✝⁴ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\ninst✝¹ : (x : M) → ENorm (TangentSpace I x)\ninst✝ : ∀ (x : M), ENormSMulClass ℝ (TangentSp... | exact biInf_le _ hf | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Geometry.Manifold.Riemannian.PathELength | {
"line": 242,
"column": 4
} | {
"line": 242,
"column": 55
} | [
{
"pp": "E✝ : Type u_1\ninst✝⁶ : NormedAddCommGroup E✝\ninst✝⁵ : NormedSpace ℝ E✝\nH : Type u_2\ninst✝⁴ : TopologicalSpace H\nI : ModelWithCorners ℝ E✝ H\nM : Type u_3\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\ninst✝¹ : (x : M) → ENorm (TangentSpace I x)\ninst✝ : ∀ (x : M), ENormSMulClass ℝ (Tange... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 945,
"column": 9
} | {
"line": 945,
"column": 72
} | [
{
"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\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\ninst✝¹ : IsManifold I (minSmoothness ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Riemannian.PathELength | {
"line": 281,
"column": 6
} | {
"line": 281,
"column": 17
} | [
{
"pp": "case ha\nE : Type u_1\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\nH : Type u_2\ninst✝⁴ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\ninst✝¹ : (x : M) → ENorm (TangentSpace I x)\ninst✝ : ∀ (x : M), ENormSMulClass ℝ (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Riemannian.Basic | {
"line": 180,
"column": 4
} | {
"line": 180,
"column": 43
} | [
{
"pp": "case refine_2\nE : Type u_1\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\nH : Type u_2\ninst✝⁴ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nn : ℕ∞ω\nM : Type u_3\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\nF : Type u_4\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSp... | exact lintegral_fderiv_lineMap_eq_edist | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Geometry.Manifold.Riemannian.Basic | {
"line": 272,
"column": 34
} | {
"line": 272,
"column": 45
} | [
{
"pp": "E : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\nH : Type u_2\ninst✝⁵ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝⁴ : TopologicalSpace M\ninst✝³ : ChartedSpace H M\ninst✝² : RiemannianBundle fun x ↦ TangentSpace I x\ninst✝¹ : IsManifold I 1 M\ninst✝ : IsCo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Riemannian.Basic | {
"line": 279,
"column": 2
} | {
"line": 288,
"column": 13
} | [
{
"pp": "E : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\nH : Type u_2\ninst✝⁵ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝⁴ : TopologicalSpace M\ninst✝³ : ChartedSpace H M\ninst✝² : RiemannianBundle fun x ↦ TangentSpace I x\ninst✝¹ : IsManifold I 1 M\ninst✝ : IsCo... | rcases eventually_norm_mfderivWithin_symm_extChartAt_comp_lt I x with ⟨C, C_pos, hC⟩
refine ⟨C, C_pos, ?_⟩
have : 𝓝 x = 𝓝 ((extChartAt I x).symm (extChartAt I x x)) := by simp
rw [this] at hC
have : ContinuousAt (extChartAt I x).symm (extChartAt I x x) := continuousAt_extChartAt_symm _
filter_upwards [nhdsW... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Manifold.Riemannian.Basic | {
"line": 279,
"column": 2
} | {
"line": 288,
"column": 13
} | [
{
"pp": "E : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\nH : Type u_2\ninst✝⁵ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝⁴ : TopologicalSpace M\ninst✝³ : ChartedSpace H M\ninst✝² : RiemannianBundle fun x ↦ TangentSpace I x\ninst✝¹ : IsManifold I 1 M\ninst✝ : IsCo... | rcases eventually_norm_mfderivWithin_symm_extChartAt_comp_lt I x with ⟨C, C_pos, hC⟩
refine ⟨C, C_pos, ?_⟩
have : 𝓝 x = 𝓝 ((extChartAt I x).symm (extChartAt I x x)) := by simp
rw [this] at hC
have : ContinuousAt (extChartAt I x).symm (extChartAt I x x) := continuousAt_extChartAt_symm _
filter_upwards [nhdsW... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Manifold.Sheaf.LocallyRingedSpace | {
"line": 61,
"column": 4
} | {
"line": 61,
"column": 20
} | [
{
"pp": "case mp\n𝕜 : Type u\ninst✝⁵ : NontriviallyNormedField 𝕜\nEM : Type u_1\ninst✝⁴ : NormedAddCommGroup EM\ninst✝³ : NormedSpace 𝕜 EM\nHM : Type u_2\ninst✝² : TopologicalSpace HM\nIM : ModelWithCorners 𝕜 EM HM\nM : Type u\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace HM M\nx : M\nf g : ↑((smoothSh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Riemannian.Basic | {
"line": 382,
"column": 4
} | {
"line": 382,
"column": 54
} | [
{
"pp": "E : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\nH : Type u_2\ninst✝⁵ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝⁴ : TopologicalSpace M\ninst✝³ : ChartedSpace H M\ninst✝² : RiemannianBundle fun x ↦ TangentSpace I x\ninst✝¹ : IsManifold I 1 M\ninst✝ : IsCo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Riemannian.Basic | {
"line": 418,
"column": 4
} | {
"line": 418,
"column": 52
} | [
{
"pp": "E : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\nH : Type u_2\ninst✝⁶ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝⁵ : TopologicalSpace M\ninst✝⁴ : ChartedSpace H M\ninst✝³ : RiemannianBundle fun x ↦ TangentSpace I x\ninst✝² : IsManifold I 1 M\ninst✝¹ : IsC... | exact ⟨u, u_mem, u_closed, hu.1.1, hu.1.2, hu.2⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Geometry.Manifold.Riemannian.Basic | {
"line": 419,
"column": 44
} | {
"line": 419,
"column": 79
} | [
{
"pp": "E : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\nH : Type u_2\ninst✝⁶ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝⁵ : TopologicalSpace M\ninst✝⁴ : ChartedSpace H M\ninst✝³ : RiemannianBundle fun x ↦ TangentSpace I x\ninst✝² : IsManifold I 1 M\ninst✝¹ : IsC... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.VectorBundle.Riemannian | {
"line": 165,
"column": 6
} | {
"line": 165,
"column": 17
} | [
{
"pp": "case a\nB✝ : Type u_1\ninst✝⁷ : TopologicalSpace B✝\nF : Type u_2\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace ℝ F\nE : B✝ → Type u_3\ninst✝⁴ : TopologicalSpace (TotalSpace F E)\ninst✝³ : (x : B✝) → NormedAddCommGroup (E x)\ninst✝² : (x : B✝) → InnerProductSpace ℝ (E x)\ninst✝¹ : FiberBundle F ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Riemannian.Basic | {
"line": 490,
"column": 37
} | {
"line": 490,
"column": 48
} | [
{
"pp": "E : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\nH : Type u_2\ninst✝⁶ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝⁵ : TopologicalSpace M\ninst✝⁴ : ChartedSpace H M\ninst✝³ : RiemannianBundle fun x ↦ TangentSpace I x\ninst✝² : IsManifold I 1 M\ninst✝¹ : IsC... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 1045,
"column": 2
} | {
"line": 1046,
"column": 71
} | [
{
"pp": "case h.e_6.h.h'x\n𝕜 : 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\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\ninst✝¹ : IsManifold... | · rw [inter_comm]
exact extChartAt_mem_closure_interior h's (mem_extChartAt_source x) | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Geometry.Manifold.VectorBundle.LocalFrame | {
"line": 171,
"column": 2
} | {
"line": 171,
"column": 30
} | [
{
"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\nF : Type u_5\ninst✝⁶ : NormedAddCo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.LocalFrame | {
"line": 207,
"column": 2
} | {
"line": 207,
"column": 25
} | [
{
"pp": "𝕜 : 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 : NormedAddC... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.LocalFrame | {
"line": 266,
"column": 2
} | {
"line": 266,
"column": 13
} | [
{
"pp": "case inr\n𝕜 : Type u_1\ninst✝¹⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹¹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹⁰ : TopologicalSpace M\ninst✝⁹ : ChartedSpace H M\nF : Type u_5\ninst✝⁸ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.Tensoriality | {
"line": 96,
"column": 25
} | {
"line": 96,
"column": 41
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹¹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹⁰ : TopologicalSpace M\ninst✝⁹ : ChartedSpace H M\nF : Type u_5\ninst✝⁸ : NormedAdd... | rw [funext this] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Manifold.VectorBundle.Tensoriality | {
"line": 96,
"column": 25
} | {
"line": 96,
"column": 41
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹¹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹⁰ : TopologicalSpace M\ninst✝⁹ : ChartedSpace H M\nF : Type u_5\ninst✝⁸ : NormedAdd... | rw [funext this] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Manifold.VectorBundle.Tensoriality | {
"line": 96,
"column": 25
} | {
"line": 96,
"column": 41
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹¹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹⁰ : TopologicalSpace M\ninst✝⁹ : ChartedSpace H M\nF : Type u_5\ninst✝⁸ : NormedAdd... | rw [funext this] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Manifold.VectorBundle.LocalFrame | {
"line": 303,
"column": 2
} | {
"line": 303,
"column": 13
} | [
{
"pp": "case inr\n𝕜 : Type u_1\ninst✝¹⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹¹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹⁰ : TopologicalSpace M\ninst✝⁹ : ChartedSpace H M\nF : Type u_5\ninst✝⁸ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.LocalFrame | {
"line": 397,
"column": 2
} | {
"line": 397,
"column": 32
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹⁴ : NormedAddCommGroup E\ninst✝¹³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹¹ : TopologicalSpace M\ninst✝¹⁰ : ChartedSpace H M\nF : Type u_5\ninst✝⁹ : NormedAd... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.LocalFrame | {
"line": 428,
"column": 2
} | {
"line": 428,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹⁴ : NormedAddCommGroup E\ninst✝¹³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹¹ : TopologicalSpace M\ninst✝¹⁰ : ChartedSpace H M\nF : Type u_5\ninst✝⁹ : NormedAd... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.LocalFrame | {
"line": 471,
"column": 4
} | {
"line": 471,
"column": 15
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹⁷ : NormedAddCommGroup E\ninst✝¹⁶ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹⁵ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹⁴ : TopologicalSpace M\ninst✝¹³ : ChartedSpace H M\nF : Type u_5\ninst✝¹² : NormedA... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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