module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable | {
"line": 561,
"column": 4
} | {
"line": 561,
"column": 15
} | {
"line": 561,
"column": 16
} | [
{
"pp": "case h\n𝕜 : Type u_1\nB : Type u_2\nF : Type u_4\nE : B → Type u_6\ninst✝¹³ : TopologicalSpace B\ninst✝¹² : TopologicalSpace (TotalSpace F E)\ninst✝¹¹ : (x : B) → TopologicalSpace (E x)\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NontriviallyNormedField 𝕜\ninst✝⁸ : NormedSpace 𝕜 F\ninst✝⁷ : FiberBundl... | [
"case h\n𝕜 : Type u_1\nB : Type u_2\nF : Type u_4\nE : B → Type u_6\ninst✝¹³ : TopologicalSpace B\ninst✝¹² : TopologicalSpace (TotalSpace F E)\ninst✝¹¹ : (x : B) → TopologicalSpace (E x)\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NontriviallyNormedField 𝕜\ninst✝⁸ : NormedSpace 𝕜 F\ninst✝⁷ : FiberBundle F E\ninst✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable | {
"line": 640,
"column": 6
} | {
"line": 640,
"column": 29
} | {
"line": 640,
"column": 29
} | [
{
"pp": "𝕜 : 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 : NormedSpace ... | [
"𝕜 : 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 : NormedSpace 𝕜 F₁\ninst✝... | inCoordinates_eq hm h'm | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 1079,
"column": 2
} | {
"line": 1079,
"column": 30
} | {
"line": 1079,
"column": 31
} | [
{
"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... | [
"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\ninst✝¹ : Normed... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 1084,
"column": 2
} | {
"line": 1084,
"column": 30
} | {
"line": 1084,
"column": 31
} | [
{
"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\nz : M\nF' : Type u_21\ninst✝¹ : Norme... | [
"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\nz : M\nF' : Type u_21\ninst✝¹ : NormedDivisionRin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 1089,
"column": 2
} | {
"line": 1089,
"column": 30
} | {
"line": 1089,
"column": 31
} | [
{
"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... | [
"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 : NormedDivisio... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 1094,
"column": 2
} | {
"line": 1094,
"column": 30
} | {
"line": 1094,
"column": 31
} | [
{
"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... | [
"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 : NormedDivisionRing F'\ni... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable | {
"line": 724,
"column": 2
} | {
"line": 724,
"column": 13
} | {
"line": 724,
"column": 14
} | [
{
"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... | [
"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 : NormedAddCommGroup F... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 1118,
"column": 2
} | {
"line": 1118,
"column": 40
} | {
"line": 1119,
"column": 2
} | [
{
"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... | [
"case e'_21\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\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.Geometry.Manifold.VectorBundle.MDifferentiable | {
"line": 734,
"column": 2
} | {
"line": 734,
"column": 13
} | {
"line": 734,
"column": 14
} | [
{
"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... | [
"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 : NormedAddCommGroup F... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.Hom | {
"line": 235,
"column": 6
} | {
"line": 235,
"column": 29
} | {
"line": 235,
"column": 29
} | [
{
"pp": "𝕜 : 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 : NormedSpace ... | [
"𝕜 : 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 : NormedSpace 𝕜 F₁\ninst✝... | inCoordinates_eq hm h'm | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Manifold.MFDeriv.NormedSpace | {
"line": 112,
"column": 2
} | {
"line": 112,
"column": 34
} | {
"line": 112,
"column": 35
} | [
{
"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... | [
"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✝¹ : NormedA... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.NormedSpace | {
"line": 120,
"column": 2
} | {
"line": 120,
"column": 34
} | {
"line": 120,
"column": 35
} | [
{
"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... | [
"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✝² : NormedA... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.NormedSpace | {
"line": 403,
"column": 2
} | {
"line": 403,
"column": 13
} | {
"line": 403,
"column": 14
} | [
{
"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... | [
"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 : NormedAddCommGroup... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.NormedSpace | {
"line": 551,
"column": 2
} | {
"line": 551,
"column": 13
} | {
"line": 551,
"column": 14
} | [
{
"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... | [
"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 : NormedAddCommGroup F\ninst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.NormedSpace | {
"line": 593,
"column": 2
} | {
"line": 593,
"column": 13
} | {
"line": 593,
"column": 14
} | [
{
"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... | [
"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 : NormedAddCommGroup F\ninst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.VectorBundle.Hom | {
"line": 111,
"column": 4
} | {
"line": 115,
"column": 19
} | {
"line": 116,
"column": 2
} | [
{
"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": 111,
"column": 4
} | {
"line": 115,
"column": 19
} | {
"line": 116,
"column": 2
} | [
{
"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.VectorField.LieBracket | {
"line": 115,
"column": 4
} | {
"line": 115,
"column": 19
} | {
"line": 116,
"column": 2
} | [
{
"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.LieBracket | {
"line": 119,
"column": 4
} | {
"line": 119,
"column": 19
} | {
"line": 121,
"column": 0
} | [
{
"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": 349,
"column": 2
} | {
"line": 349,
"column": 13
} | {
"line": 349,
"column": 14
} | [
{
"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... | [
"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 : TopologicalSpace H'\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorField.Pullback | {
"line": 558,
"column": 2
} | {
"line": 558,
"column": 13
} | {
"line": 558,
"column": 14
} | [
{
"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... | [
"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 : TopologicalSpace H'\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorField.Pullback | {
"line": 607,
"column": 2
} | {
"line": 607,
"column": 13
} | {
"line": 607,
"column": 14
} | [
{
"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... | [
"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 : TopologicalSpace H'\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.LocalSourceTargetProperty | {
"line": 194,
"column": 4
} | {
"line": 194,
"column": 15
} | {
"line": 194,
"column": 16
} | [
{
"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... | [
"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 : ModelWithCorn... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.ContMDiffMFDeriv | {
"line": 167,
"column": 43
} | {
"line": 167,
"column": 54
} | {
"line": 167,
"column": 55
} | [
{
"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... | [
"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\ninst✝⁹ : N... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.LocalSourceTargetProperty | {
"line": 241,
"column": 2
} | {
"line": 243,
"column": 85
} | {
"line": 244,
"column": 2
} | [
{
"pp": "case source_subset_preimage_source\n𝕜 : Type u_1\nE : Type u_2\nE' : Type u_3\nF : Type u_4\nF' : Type u_5\nH : Type u_6\nH' : Type u_7\nG : Type u_8\nG' : Type u_9\ninst✝²⁴ : NontriviallyNormedField 𝕜\ninst✝²³ : NormedAddCommGroup E\ninst✝²² : NormedSpace 𝕜 E\ninst✝²¹ : NormedAddCommGroup E'\ninst✝... | [
"case property\n𝕜 : Type u_1\nE : Type u_2\nE' : Type u_3\nF : Type u_4\nF' : Type u_5\nH : Type u_6\nH' : Type u_7\nG : Type u_8\nG' : Type u_9\ninst✝²⁴ : NontriviallyNormedField 𝕜\ninst✝²³ : NormedAddCommGroup E\ninst✝²² : NormedSpace 𝕜 E\ninst✝²¹ : NormedAddCommGroup E'\ninst✝²⁰ : NormedSpace 𝕜 E'\ninst✝¹⁹ :... | · simp only [OpenPartialHomeomorph.prod_toPartialHomeomorph, PartialEquiv.prod_source,
preimage_prod_map_prod]
exact prod_mono hf.source_subset_preimage_source hg.source_subset_preimage_source | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Geometry.Manifold.ContMDiffMFDeriv | {
"line": 171,
"column": 4
} | {
"line": 173,
"column": 62
} | {
"line": 174,
"column": 2
} | [
{
"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": 580,
"column": 80
} | {
"line": 580,
"column": 91
} | {
"line": 580,
"column": 92
} | [
{
"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... | [
"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 : TopologicalSpace H'\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Instances.Real | {
"line": 150,
"column": 2
} | {
"line": 150,
"column": 52
} | {
"line": 150,
"column": 53
} | [
{
"pp": "n : 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}",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Real",
"congrArg",
"PartialOrder.toPreorder",
... | [
"n : ℕ\np : ℝ≥0∞\na : ℝ\ni : Fin n\ny : PiLp p fun x ↦ ℝ\n⊢ a ≤ y.ofLp i ∧ y.ofLp i ≤ a ↔ a = y.ofLp i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Immersion | {
"line": 373,
"column": 2
} | {
"line": 373,
"column": 81
} | {
"line": 374,
"column": 2
} | [
{
"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'... | [
"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''\ninst✝²² :... | 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": 374,
"column": 30
} | {
"line": 374,
"column": 41
} | {
"line": 374,
"column": 42
} | [
{
"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✝... | [
"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✝²² : NormedS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Immersion | {
"line": 374,
"column": 74
} | {
"line": 374,
"column": 85
} | {
"line": 374,
"column": 86
} | [
{
"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✝... | [
"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✝²² : NormedS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.ContMDiffMFDeriv | {
"line": 183,
"column": 4
} | {
"line": 183,
"column": 15
} | {
"line": 183,
"column": 16
} | [
{
"pp": "case 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' :... | [
"case 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' : Type u_5\ni... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.ContMDiffMFDeriv | {
"line": 183,
"column": 4
} | {
"line": 183,
"column": 18
} | {
"line": 184,
"column": 2
} | [
{
"pp": "case 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": 183,
"column": 4
} | {
"line": 183,
"column": 18
} | {
"line": 184,
"column": 2
} | [
{
"pp": "case 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": 183,
"column": 4
} | {
"line": 183,
"column": 18
} | {
"line": 184,
"column": 2
} | [
{
"pp": "case 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.Instances.Real | {
"line": 392,
"column": 6
} | {
"line": 392,
"column": 31
} | {
"line": 392,
"column": 32
} | [
{
"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",
"ppTerm": "?neg✝",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 590,
"column": 6
} | {
"line": 590,
"column": 83
} | {
"line": 591,
"column": 4
} | [
{
"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 (mdifferentiableWithinAt_extChartAt_symm h'''y).mono inter_subset_right | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Geometry.Manifold.ContMDiffMFDeriv | {
"line": 184,
"column": 4
} | {
"line": 184,
"column": 15
} | {
"line": 184,
"column": 16
} | [
{
"pp": "case 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' :... | [
"case 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' : Type u_5\ni... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 590,
"column": 6
} | {
"line": 590,
"column": 83
} | {
"line": 591,
"column": 4
} | [
{
"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 (mdifferentiableWithinAt_extChartAt_symm h'''y).mono inter_subset_right | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 590,
"column": 6
} | {
"line": 590,
"column": 83
} | {
"line": 591,
"column": 4
} | [
{
"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 (mdifferentiableWithinAt_extChartAt_symm h'''y).mono inter_subset_right | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Manifold.ContMDiffMFDeriv | {
"line": 197,
"column": 2
} | {
"line": 197,
"column": 71
} | {
"line": 199,
"column": 0
} | [
{
"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.Immersion | {
"line": 454,
"column": 38
} | {
"line": 454,
"column": 73
} | {
"line": 454,
"column": 73
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁷ : NontriviallyNormedField 𝕜\nE : Type u_2\nE''' : Type u_4\nE'' : Type u\nF : Type u_5\ninst✝¹⁶ : NormedAddCommGroup E\ninst✝¹⁵ : NormedSpace 𝕜 E\ninst✝¹⁴ : NormedAddCommGroup E''\ninst✝¹³ : NormedSpace 𝕜 E''\ninst✝¹² : NormedAddCommGroup E'''\ninst✝¹¹ : NormedSpace 𝕜 E'''\ni... | [] | by simp [mem_chart_source H x, hxt] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Geometry.Manifold.ContMDiffMFDeriv | {
"line": 308,
"column": 2
} | {
"line": 308,
"column": 33
} | {
"line": 309,
"column": 2
} | [
{
"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... | [
"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\ninst✝⁴ : Normed... | rw [← contMDiffOn_univ] at hf ⊢ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Manifold.Instances.Icc | {
"line": 86,
"column": 6
} | {
"line": 86,
"column": 17
} | {
"line": 86,
"column": 18
} | [
{
"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}",
"ppTerm": "?pos.hx✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Real",
... | [
"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⊢ x ≤ ↑z"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Instances.Icc | {
"line": 89,
"column": 6
} | {
"line": 89,
"column": 17
} | {
"line": 89,
"column": 18
} | [
{
"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}",
"ppTerm": "?m.241",
"assigned": true,
"usedConstants": [
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
... | [
"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⊢ ↑z < y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Instances.Icc | {
"line": 102,
"column": 6
} | {
"line": 102,
"column": 17
} | {
"line": 102,
"column": 18
} | [
{
"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}",
"ppTerm": "?neg.hx✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Real",
... | [
"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⊢ ↑z ≤ y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Instances.Icc | {
"line": 105,
"column": 6
} | {
"line": 105,
"column": 17
} | {
"line": 105,
"column": 18
} | [
{
"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}",
"ppTerm": "?m.451",
"assigned": true,
"usedConstants": [
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
... | [
"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⊢ x < ↑z"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Instances.Icc | {
"line": 162,
"column": 2
} | {
"line": 162,
"column": 35
} | {
"line": 163,
"column": 2
} | [
{
"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... | [
"case refine_1\nE : 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)\nhf : MDiffAt[Icc x y] (f ∘... | refine ⟨fun hf ↦ ?_, fun hf ↦ ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Geometry.Manifold.Instances.Sphere | {
"line": 134,
"column": 4
} | {
"line": 134,
"column": 71
} | {
"line": 134,
"column": 72
} | [
{
"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",
"ppTerm": "?m.198",
"assigned": false,
"... | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Instances.Sphere | {
"line": 146,
"column": 4
} | {
"line": 146,
"column": 81
} | {
"line": 147,
"column": 2
} | [
{
"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",
"ppTerm": "?m.202",
"assigned": true,
"usedConstants": [
"ContinuousLinearMap.comp",
"HasFDerivAt",
"Nor... | [] | 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
} | {
"line": 196,
"column": 16
} | [
{
"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",
"ppTerm": "?m.118",
"assigned": true,
"usedConstants": [
"one_pow",
... | [
"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⊢ (‖↑w‖ ^ 2 + 4)⁻¹ * (‖↑w‖ ^ 2 - 4) < 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Instances.Sphere | {
"line": 197,
"column": 4
} | {
"line": 197,
"column": 15
} | {
"line": 197,
"column": 16
} | [
{
"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",
"ppTerm": "?m.49",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Submodule... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : InnerProductSpace ℝ E\nv : E\nhv : ‖v‖ = 1\nw : ↥(ℝ ∙ v)ᗮ\n⊢ ‖(‖↑w‖ ^ 2 + 4)⁻¹ • 4 • ↑w + (‖↑w‖ ^ 2 + 4)⁻¹ • (‖↑w‖ ^ 2 - 4) • v‖ = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Instances.Sphere | {
"line": 222,
"column": 4
} | {
"line": 222,
"column": 16
} | {
"line": 224,
"column": 2
} | [
{
"pp": "case e'_3.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.orthogonalProjectionOnto ↑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.IntegralCurve.Basic | {
"line": 126,
"column": 4
} | {
"line": 126,
"column": 53
} | {
"line": 126,
"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": 230,
"column": 2
} | {
"line": 231,
"column": 33
} | {
"line": 232,
"column": 2
} | [
{
"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.orthogonalProjectionOnto ↑x\nsplit : ↑x = a • v + ↑y\nhvy : ⟪v, ↑y⟫_ℝ = 0\npythag : 1 = a ^ 2 + ‖y‖ ^ 2\nha : 0 < 1 - a... | [
"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.orthogonalProjectionOnto ↑x\nsplit : ↑x = a • v + ↑y\nhvy : ⟪v, ↑y⟫_ℝ = 0\npythag : 1 = a ^ 2 + ‖y‖ ^ 2\nha : 0 < 1 - a\n⊢ ((|2| / ... | · field_simp
linear_combination 4 * pythag | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Geometry.Manifold.Instances.Sphere | {
"line": 357,
"column": 27
} | {
"line": 357,
"column": 38
} | {
"line": 357,
"column": 39
} | [
{
"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",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
"stereographic'",
"Eq.mpr",
"Real",
... | [
"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 = -v"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IntegralCurve.Transform | {
"line": 44,
"column": 18
} | {
"line": 44,
"column": 98
} | {
"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 : ... | [
"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 : ℝ\nht : t ∈ ... | ← ContinuousLinearMap.comp_id (ContinuousLinearMap.smulRight 1 (v (γ (t + dt)))) | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Manifold.Instances.Sphere | {
"line": 459,
"column": 31
} | {
"line": 459,
"column": 42
} | {
"line": 459,
"column": 43
} | [
{
"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✝... | [
"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✝¹ : IsManifo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IntegralCurve.Transform | {
"line": 86,
"column": 2
} | {
"line": 86,
"column": 13
} | {
"line": 86,
"column": 14
} | [
{
"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... | [
"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⊢ IsMIntegralCurveO... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Instances.Sphere | {
"line": 542,
"column": 2
} | {
"line": 542,
"column": 38
} | {
"line": 542,
"column": 39
} | [
{
"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... | [
"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.val) (ℝ ∙ ↑(-... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 622,
"column": 2
} | {
"line": 622,
"column": 15
} | {
"line": 623,
"column": 2
} | [
{
"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 :... | [
"case h'f\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 : Topologica... | · exact hsymm | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 628,
"column": 6
} | {
"line": 629,
"column": 26
} | {
"line": 630,
"column": 4
} | [
{
"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": 628,
"column": 6
} | {
"line": 629,
"column": 26
} | {
"line": 630,
"column": 4
} | [
{
"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": 628,
"column": 6
} | {
"line": 629,
"column": 26
} | {
"line": 630,
"column": 4
} | [
{
"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.Riemannian.PathELength | {
"line": 70,
"column": 67
} | {
"line": 70,
"column": 85
} | {
"line": 72,
"column": 0
} | [
{
"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
} | {
"line": 72,
"column": 0
} | [
{
"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
} | {
"line": 72,
"column": 0
} | [
{
"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
} | {
"line": 88,
"column": 0
} | [
{
"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
} | {
"line": 88,
"column": 0
} | [
{
"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
} | {
"line": 88,
"column": 0
} | [
{
"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
} | {
"line": 103,
"column": 53
} | [
{
"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 ≤ ... | [
"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 ≤ b'\n⊢ ∫⁻ (t ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Riemannian.PathELength | {
"line": 233,
"column": 26
} | {
"line": 233,
"column": 45
} | {
"line": 234,
"column": 2
} | [
{
"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
} | {
"line": 242,
"column": 56
} | [
{
"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... | [
"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 (TangentSpace I x)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Riemannian.PathELength | {
"line": 281,
"column": 6
} | {
"line": 281,
"column": 17
} | {
"line": 281,
"column": 18
} | [
{
"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 (... | [
"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 (TangentSpace... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 682,
"column": 4
} | {
"line": 683,
"column": 38
} | {
"line": 684,
"column": 4
} | [
{
"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... | [
"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 : TopologicalSpace H'\n... | 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.VectorField.LieBracket | {
"line": 714,
"column": 32
} | {
"line": 714,
"column": 43
} | {
"line": 714,
"column": 44
} | [
{
"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... | [
"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 : TopologicalSpace H'\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Riemannian.Basic | {
"line": 180,
"column": 4
} | {
"line": 180,
"column": 43
} | {
"line": 182,
"column": 0
} | [
{
"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
} | {
"line": 272,
"column": 46
} | [
{
"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... | [
"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✝ : IsContinuousRiem... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Riemannian.Basic | {
"line": 279,
"column": 2
} | {
"line": 288,
"column": 13
} | {
"line": 290,
"column": 0
} | [
{
"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
} | {
"line": 290,
"column": 0
} | [
{
"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.VectorField.LieBracket | {
"line": 853,
"column": 9
} | {
"line": 853,
"column": 71
} | {
"line": 853,
"column": 72
} | [
{
"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 ... | [
"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 𝕜 2) M\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.VectorBundle.Riemannian | {
"line": 165,
"column": 6
} | {
"line": 165,
"column": 17
} | {
"line": 165,
"column": 18
} | [
{
"pp": "B✝ : 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 E\ninst✝... | [
"B✝ : 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 E\ninst✝ : VectorBun... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Sheaf.LocallyRingedSpace | {
"line": 61,
"column": 4
} | {
"line": 61,
"column": 20
} | {
"line": 61,
"column": 21
} | [
{
"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... | [
"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 : ↑((smoothSheafCommRing ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Riemannian.Basic | {
"line": 382,
"column": 4
} | {
"line": 382,
"column": 54
} | {
"line": 382,
"column": 55
} | [
{
"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... | [
"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✝ : IsContinuousRiem... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 943,
"column": 9
} | {
"line": 943,
"column": 72
} | {
"line": 943,
"column": 73
} | [
{
"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 ... | [
"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 𝕜 3) M\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Riemannian.Basic | {
"line": 418,
"column": 4
} | {
"line": 418,
"column": 52
} | {
"line": 419,
"column": 2
} | [
{
"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
} | {
"line": 419,
"column": 80
} | [
{
"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... | [
"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 : IsContinuousRie... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Submersion | {
"line": 349,
"column": 2
} | {
"line": 349,
"column": 81
} | {
"line": 350,
"column": 2
} | [
{
"pp": "case h\n𝕜 : Type u_1\nE' : Type u_2\nE'' : Type u_3\nE''' : Type u_4\nF : Type u_5\nF' : Type u_6\nH : Type u_7\nH' : Type u_8\nG : Type u_9\nG' : Type u_10\nE : Type u\ninst✝²⁸ : NontriviallyNormedField 𝕜\ninst✝²⁷ : NormedAddCommGroup E\ninst✝²⁶ : NormedSpace 𝕜 E\ninst✝²⁵ : NormedAddCommGroup E'\ni... | [
"case h\n𝕜 : Type u_1\nE' : Type u_2\nE'' : Type u_3\nE''' : Type u_4\nF : Type u_5\nF' : Type u_6\nH : Type u_7\nH' : Type u_8\nG : Type u_9\nG' : Type u_10\nE : Type u\ninst✝²⁸ : NontriviallyNormedField 𝕜\ninst✝²⁷ : NormedAddCommGroup E\ninst✝²⁶ : NormedSpace 𝕜 E\ninst✝²⁵ : NormedAddCommGroup E'\ninst✝²⁴ : Nor... | 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.Submersion | {
"line": 350,
"column": 30
} | {
"line": 350,
"column": 41
} | {
"line": 350,
"column": 42
} | [
{
"pp": "𝕜 : Type u_1\nE' : Type u_2\nE'' : Type u_3\nE''' : Type u_4\nF : Type u_5\nF' : Type u_6\nH : Type u_7\nH' : Type u_8\nG : Type u_9\nG' : Type u_10\nE : Type u\ninst✝²⁸ : NontriviallyNormedField 𝕜\ninst✝²⁷ : NormedAddCommGroup E\ninst✝²⁶ : NormedSpace 𝕜 E\ninst✝²⁵ : NormedAddCommGroup E'\ninst✝²⁴ :... | [
"𝕜 : Type u_1\nE' : Type u_2\nE'' : Type u_3\nE''' : Type u_4\nF : Type u_5\nF' : Type u_6\nH : Type u_7\nH' : Type u_8\nG : Type u_9\nG' : Type u_10\nE : Type u\ninst✝²⁸ : NontriviallyNormedField 𝕜\ninst✝²⁷ : NormedAddCommGroup E\ninst✝²⁶ : NormedSpace 𝕜 E\ninst✝²⁵ : NormedAddCommGroup E'\ninst✝²⁴ : NormedSpace... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Submersion | {
"line": 350,
"column": 74
} | {
"line": 350,
"column": 85
} | {
"line": 350,
"column": 86
} | [
{
"pp": "𝕜 : Type u_1\nE' : Type u_2\nE'' : Type u_3\nE''' : Type u_4\nF : Type u_5\nF' : Type u_6\nH : Type u_7\nH' : Type u_8\nG : Type u_9\nG' : Type u_10\nE : Type u\ninst✝²⁸ : NontriviallyNormedField 𝕜\ninst✝²⁷ : NormedAddCommGroup E\ninst✝²⁶ : NormedSpace 𝕜 E\ninst✝²⁵ : NormedAddCommGroup E'\ninst✝²⁴ :... | [
"𝕜 : Type u_1\nE' : Type u_2\nE'' : Type u_3\nE''' : Type u_4\nF : Type u_5\nF' : Type u_6\nH : Type u_7\nH' : Type u_8\nG : Type u_9\nG' : Type u_10\nE : Type u\ninst✝²⁸ : NontriviallyNormedField 𝕜\ninst✝²⁷ : NormedAddCommGroup E\ninst✝²⁶ : NormedSpace 𝕜 E\ninst✝²⁵ : NormedAddCommGroup E'\ninst✝²⁴ : NormedSpace... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Submersion | {
"line": 661,
"column": 70
} | {
"line": 663,
"column": 35
} | {
"line": 665,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\nH : Type u_7\nE : Type u\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_11\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\nn : ℕ∞ω\ninst✝ : IsManifold I n M\n⊢ I... | [] | by
use PUnit, by infer_instance, by infer_instance
exact IsSubmersionOfComplement.id | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Geometry.Manifold.Riemannian.Basic | {
"line": 490,
"column": 37
} | {
"line": 490,
"column": 48
} | {
"line": 490,
"column": 49
} | [
{
"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... | [
"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 : IsContinuousRie... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.LocalFrame | {
"line": 171,
"column": 2
} | {
"line": 171,
"column": 30
} | {
"line": 171,
"column": 31
} | [
{
"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... | [
"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 : NormedAddCommGroup F\ni... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.LocalFrame | {
"line": 207,
"column": 2
} | {
"line": 207,
"column": 25
} | {
"line": 207,
"column": 26
} | [
{
"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... | [
"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 : NormedAddCommGroup F\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.Tensoriality | {
"line": 97,
"column": 25
} | {
"line": 97,
"column": 41
} | {
"line": 98,
"column": 4
} | [
{
"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": 97,
"column": 25
} | {
"line": 97,
"column": 41
} | {
"line": 98,
"column": 4
} | [
{
"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": 97,
"column": 25
} | {
"line": 97,
"column": 41
} | {
"line": 98,
"column": 4
} | [
{
"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": 266,
"column": 2
} | {
"line": 266,
"column": 13
} | {
"line": 266,
"column": 14
} | [
{
"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 :... | [
"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 : NormedAddCo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.LocalFrame | {
"line": 303,
"column": 2
} | {
"line": 303,
"column": 13
} | {
"line": 303,
"column": 14
} | [
{
"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 :... | [
"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 : NormedAddCo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.LocalFrame | {
"line": 397,
"column": 2
} | {
"line": 397,
"column": 32
} | {
"line": 398,
"column": 4
} | [
{
"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... | [
"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 : NormedAddCommGroup F... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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