module stringlengths 16 90 | startPos dict | endPos dict | nextStartPos dict | goals listlengths 0 96 | goalsAfter listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 375
values | kind stringclasses 379
values |
|---|---|---|---|---|---|---|---|---|
Mathlib.Geometry.Euclidean.NinePointCircle | {
"line": 114,
"column": 4
} | {
"line": 114,
"column": 31
} | {
"line": 114,
"column": 32
} | [
{
"pp": "case right\nV : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nn : ℕ\ninst✝ : NeZero n\ns : Simplex ℝ P n\n⊢ ∀ (y : Fin (n + 1)), s.medial.points y ∈ Metric.sphere s.ninePointCircle.center s.ninePointCircle.ra... | [
"case right\nV : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nn : ℕ\ninst✝ : NeZero n\ns : Simplex ℝ P n\n⊢ ∀ (y : Fin (n + 1)), s.faceOppositeCentroid y ∈ s.ninePointCircle"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.NinePointCircle | {
"line": 126,
"column": 23
} | {
"line": 126,
"column": 34
} | {
"line": 126,
"column": 35
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nm n : ℕ\ns : Simplex ℝ P n\ne : Fin (n + 1) ≃ Fin (m + 1)\n⊢ n = m",
"ppTerm": "?m.54",
"assigned": false,
"usedConstants": [],
"usedFVars": []... | [
"V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nm n : ℕ\ns : Simplex ℝ P n\ne : Fin (n + 1) ≃ Fin (m + 1)\n⊢ n = m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.Similarity | {
"line": 115,
"column": 2
} | {
"line": 115,
"column": 46
} | {
"line": 115,
"column": 47
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nP₁ : Type u_3\nP₂ : Type u_4\ninst✝¹ : PseudoEMetricSpace P₁\ninst✝ : PseudoEMetricSpace P₂\nf : ι' ≃ ι\nv₁ : ι → P₁\nv₂ : ι → P₂\nr : ℝ≥0\nhr : r ≠ 0\nh : ∀ (i₁ i₂ : ι'), edist ((v₁ ∘ ⇑f) i₁) ((v₁ ∘ ⇑f) i₂) = ↑r * edist ((v₂ ∘ ⇑f) i₁) ((v₂ ∘ ⇑f) i₂)\ni₁ i₂ : ι\n⊢ edist (v₁... | [
"ι : Type u_1\nι' : Type u_2\nP₁ : Type u_3\nP₂ : Type u_4\ninst✝¹ : PseudoEMetricSpace P₁\ninst✝ : PseudoEMetricSpace P₂\nf : ι' ≃ ι\nv₁ : ι → P₁\nv₂ : ι → P₂\nr : ℝ≥0\nhr : r ≠ 0\nh : ∀ (i₁ i₂ : ι'), edist ((v₁ ∘ ⇑f) i₁) ((v₁ ∘ ⇑f) i₂) = ↑r * edist ((v₂ ∘ ⇑f) i₁) ((v₂ ∘ ⇑f) i₂)\ni₁ i₂ : ι\n⊢ edist (v₁ i₁) (v₁ i₂)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.NinePointCircle | {
"line": 153,
"column": 28
} | {
"line": 153,
"column": 39
} | {
"line": 153,
"column": 40
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\ns : Simplex ℝ P n\ni : Fin (n + 1)\nhn : ¬n = 0\n⊢ ↑n ≠ 0",
"ppTerm": "?m.168",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"... | [
"V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\ns : Simplex ℝ P n\ni : Fin (n + 1)\nhn : ¬n = 0\n⊢ ¬n = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.MongePoint | {
"line": 92,
"column": 27
} | {
"line": 92,
"column": 38
} | {
"line": 92,
"column": 39
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nm n : ℕ\ns : Simplex ℝ P n\ne : Fin (n + 1) ≃ Fin (m + 1)\n⊢ n = m",
"ppTerm": "?m.53",
"assigned": false,
"usedConstants": [],
"usedFVars": []... | [
"V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nm n : ℕ\ns : Simplex ℝ P n\ne : Fin (n + 1) ≃ Fin (m + 1)\n⊢ n = m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.NinePointCircle | {
"line": 176,
"column": 55
} | {
"line": 176,
"column": 80
} | {
"line": 176,
"column": 81
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\nhn : NeZero n\ns : Simplex ℝ P n\ni : Fin (n + 1)\nhn1 : ¬n = 1\nhltn : 1 < n\nhnsub1 : ↑(n - 1) = ↑n - 1\n⊢ ↑n - 1 ≠ 0",
"ppTerm": "?m.370",
"a... | [
"V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\nhn : NeZero n\ns : Simplex ℝ P n\ni : Fin (n + 1)\nhn1 : ¬n = 1\nhltn : 1 < n\nhnsub1 : ↑(n - 1) = ↑n - 1\n⊢ ¬n = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.NinePointCircle | {
"line": 182,
"column": 50
} | {
"line": 182,
"column": 61
} | {
"line": 182,
"column": 62
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\nhn : NeZero n\ns : Simplex ℝ P n\ni : Fin (n + 1)\nhn1 : ¬n = 1\nhltn : 1 < n\nhnsub1 : ↑(n - 1) = ↑n - 1\n⊢ ↑n ≠ 0",
"ppTerm": "?m.548",
"assig... | [
"V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\nhn : NeZero n\ns : Simplex ℝ P n\ni : Fin (n + 1)\nhn1 : ¬n = 1\nhltn : 1 < n\nhnsub1 : ↑(n - 1) = ↑n - 1\n⊢ ¬n = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.MongePoint | {
"line": 280,
"column": 27
} | {
"line": 280,
"column": 38
} | {
"line": 280,
"column": 39
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nm n : ℕ\ns : Simplex ℝ P (n + 2)\ne : Fin (n + 3) ≃ Fin (m + 3)\ni₁ i₂ : Fin (m + 3)\n⊢ n = m",
"ppTerm": "?m.73",
"assigned": false,
"usedConstant... | [
"V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nm n : ℕ\ns : Simplex ℝ P (n + 2)\ne : Fin (n + 3) ≃ Fin (m + 3)\ni₁ i₂ : Fin (m + 3)\n⊢ n = m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.Power | {
"line": 188,
"column": 4
} | {
"line": 188,
"column": 54
} | {
"line": 188,
"column": 55
} | [
{
"pp": "V : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\nP : Type u_2\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p₃ p₄ p : P\nh : dist p₁ p * dist p₂ p = dist p₃ p * dist p₄ p\nhp₁p₂ : ∠ p₁ p p₂ = π\nhp₃p₄ : ∠ p₃ p p₄ = π\nhn : ¬Collinear ℝ {p₁, p, p₃}\nhp₁p₂_sbtw :... | [
"V : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\nP : Type u_2\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p₃ p₄ p : P\nh : dist p₁ p * dist p₂ p = dist p₃ p * dist p₄ p\nhp₁p₂ : ∠ p₁ p p₂ = π\nhp₃p₄ : ∠ p₃ p p₄ = π\nhn : ¬Collinear ℝ {p₁, p, p₃}\nhp₁p₂_sbtw : Sbtw ℝ p₁ p... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.Power | {
"line": 197,
"column": 4
} | {
"line": 197,
"column": 58
} | {
"line": 197,
"column": 59
} | [
{
"pp": "V : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\nP : Type u_2\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p₃ p₄ p : P\nh : dist p₁ p * dist p₂ p = dist p₃ p * dist p₄ p\nhp₁p₂ : ∠ p₁ p p₂ = π\nhp₃p₄ : ∠ p₃ p p₄ = π\nhn : ¬Collinear ℝ {p₁, p, p₃}\nhp₁p₂_sbtw :... | [
"V : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\nP : Type u_2\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p₃ p₄ p : P\nh : dist p₁ p * dist p₂ p = dist p₃ p * dist p₄ p\nhp₁p₂ : ∠ p₁ p p₂ = π\nhp₃p₄ : ∠ p₃ p p₄ = π\nhn : ¬Collinear ℝ {p₁, p, p₃}\nhp₁p₂_sbtw : Sbtw ℝ p₁ p... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Group.Growth.QuotientInter | {
"line": 35,
"column": 29
} | {
"line": 35,
"column": 40
} | {
"line": 35,
"column": 41
} | [
{
"pp": "G : Type u_1\ninst✝³ : Group G\ninst✝² : DecidableEq G\nH : Subgroup G\ninst✝¹ : DecidablePred fun x ↦ x ∈ H\ninst✝ : H.Normal\nA : Finset G\nm n : ℕ\nπ : G →* G ⧸ H := QuotientGroup.mk' H\nφ : G ⧸ H → G := invFunOn (⇑π) (↑A ^ m)\nhφ : Set.InjOn φ (⇑π '' ↑A ^ m)\na : G ⧸ H\nha : a ∈ ⇑π '' ↑A ^ m\n⊢ ∃ a... | [
"G : Type u_1\ninst✝³ : Group G\ninst✝² : DecidableEq G\nH : Subgroup G\ninst✝¹ : DecidablePred fun x ↦ x ∈ H\ninst✝ : H.Normal\nA : Finset G\nm n : ℕ\nπ : G →* G ⧸ H := QuotientGroup.mk' H\nφ : G ⧸ H → G := invFunOn (⇑π) (↑A ^ m)\nhφ : Set.InjOn φ (⇑π '' ↑A ^ m)\na : G ⧸ H\nha : a ∈ ⇑π '' ↑A ^ m\n⊢ ∃ a ∈ ?m.112, ?... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Group.Growth.QuotientInter | {
"line": 37,
"column": 4
} | {
"line": 37,
"column": 15
} | {
"line": 37,
"column": 16
} | [
{
"pp": "G : Type u_1\ninst✝³ : Group G\ninst✝² : DecidableEq G\nH : Subgroup G\ninst✝¹ : DecidablePred fun x ↦ x ∈ H\ninst✝ : H.Normal\nA : Finset G\nm n : ℕ\nπ : G →* G ⧸ H := QuotientGroup.mk' H\nφ : G ⧸ H → G := invFunOn (⇑π) (↑A ^ m)\nhφ : Set.InjOn φ (⇑π '' ↑A ^ m)\na : G ⧸ H\nha : a ∈ ⇑π '' ↑A ^ m\nthis ... | [
"G : Type u_1\ninst✝³ : Group G\ninst✝² : DecidableEq G\nH : Subgroup G\ninst✝¹ : DecidablePred fun x ↦ x ∈ H\ninst✝ : H.Normal\nA : Finset G\nm n : ℕ\nπ : G →* G ⧸ H := QuotientGroup.mk' H\nφ : G ⧸ H → G := invFunOn (⇑π) (↑A ^ m)\nhφ : Set.InjOn φ (⇑π '' ↑A ^ m)\na : G ⧸ H\nha : a ∈ ⇑π '' ↑A ^ m\nthis : invFunOn (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Group.Growth.QuotientInter | {
"line": 38,
"column": 72
} | {
"line": 38,
"column": 83
} | {
"line": 38,
"column": 84
} | [
{
"pp": "G : Type u_1\ninst✝³ : Group G\ninst✝² : DecidableEq G\nH : Subgroup G\ninst✝¹ : DecidablePred fun x ↦ x ∈ H\ninst✝ : H.Normal\nA : Finset G\nm n : ℕ\nπ : G →* G ⧸ H := QuotientGroup.mk' H\nφ : G ⧸ H → G := invFunOn (⇑π) (↑A ^ m)\nhφ : Set.InjOn φ (⇑π '' ↑A ^ m)\nhφA : ∀ {a : G ⧸ H}, a ∈ ⇑π '' ↑A ^ m →... | [
"G : Type u_1\ninst✝³ : Group G\ninst✝² : DecidableEq G\nH : Subgroup G\ninst✝¹ : DecidablePred fun x ↦ x ∈ H\ninst✝ : H.Normal\nA : Finset G\nm n : ℕ\nπ : G →* G ⧸ H := QuotientGroup.mk' H\nφ : G ⧸ H → G := invFunOn (⇑π) (↑A ^ m)\nhφ : Set.InjOn φ (⇑π '' ↑A ^ m)\nhφA : ∀ {a : G ⧸ H}, a ∈ ⇑π '' ↑A ^ m → φ a ∈ A ^ m... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Group.Growth.LinearLowerBound | {
"line": 74,
"column": 40
} | {
"line": 74,
"column": 68
} | {
"line": 75,
"column": 4
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nX : Finset G\nhX₁ : 1 ∈ X\nhX : X.Nontrivial\nn : ℕ\nhn : n ∈ {n | ↑X ^ (n - 1) ≠ ↑(closure ↑X)}\nm : ℕ\nhmn : m ≤ n\nhm : ↑X ^ (m - 1) = ↑(closure ↑X)\nhm₀ : m > 0\n⊢ ↑X ^ (n - 1) = ↑X ^ (n - m) * ↑X ^ (m - 1)",
"ppTerm": "?m.165",
"assign... | [] | rw [← pow_add]; congr 1; lia | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Group.Growth.LinearLowerBound | {
"line": 74,
"column": 40
} | {
"line": 74,
"column": 68
} | {
"line": 75,
"column": 4
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nX : Finset G\nhX₁ : 1 ∈ X\nhX : X.Nontrivial\nn : ℕ\nhn : n ∈ {n | ↑X ^ (n - 1) ≠ ↑(closure ↑X)}\nm : ℕ\nhmn : m ≤ n\nhm : ↑X ^ (m - 1) = ↑(closure ↑X)\nhm₀ : m > 0\n⊢ ↑X ^ (n - 1) = ↑X ^ (n - m) * ↑X ^ (m - 1)",
"ppTerm": "?m.165",
"assign... | [] | rw [← pow_add]; congr 1; lia | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Group.Growth.QuotientInter | {
"line": 52,
"column": 8
} | {
"line": 52,
"column": 71
} | {
"line": 52,
"column": 72
} | [
{
"pp": "G : Type u_1\ninst✝³ : Group G\ninst✝² : DecidableEq G\nH : Subgroup G\ninst✝¹ : DecidablePred fun x ↦ x ∈ H\ninst✝ : H.Normal\nA : Finset G\nm n : ℕ\nπ : G →* G ⧸ H := QuotientGroup.mk' H\nφ : G ⧸ H → G := invFunOn (⇑π) (↑A ^ m)\nhφ : Set.InjOn φ (⇑π '' ↑A ^ m)\nhφA : ∀ {a : G ⧸ H}, a ∈ ⇑π '' ↑A ^ m →... | [
"G : Type u_1\ninst✝³ : Group G\ninst✝² : DecidableEq G\nH : Subgroup G\ninst✝¹ : DecidablePred fun x ↦ x ∈ H\ninst✝ : H.Normal\nA : Finset G\nm n : ℕ\nπ : G →* G ⧸ H := QuotientGroup.mk' H\nφ : G ⧸ H → G := invFunOn (⇑π) (↑A ^ m)\nhφ : Set.InjOn φ (⇑π '' ↑A ^ m)\nhφA : ∀ {a : G ⧸ H}, a ∈ ⇑π '' ↑A ^ m → φ a ∈ A ^ m... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Group.Growth.LinearLowerBound | {
"line": 84,
"column": 2
} | {
"line": 84,
"column": 17
} | {
"line": 84,
"column": 18
} | [
{
"pp": "case inr\nG : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nX : Finset G\nhX₁ : 1 ∈ X\nhXclosure : (↑(closure ↑X)).Infinite\nhX : X.Nontrivial\nh : ∀ (n : ℕ), ↑X ^ (n - 1) ≠ ↑(closure ↑X)\n⊢ StrictMono fun n ↦ X ^ n",
"ppTerm": "?inr",
"assigned": false,
"usedConstants": [],
"usedF... | [
"case inr\nG : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nX : Finset G\nhX₁ : 1 ∈ X\nhXclosure : (↑(closure ↑X)).Infinite\nhX : X.Nontrivial\nh : ∀ (n : ℕ), ↑X ^ (n - 1) ≠ ↑(closure ↑X)\n⊢ StrictMono fun n ↦ X ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 140,
"column": 7
} | {
"line": 140,
"column": 46
} | {
"line": 140,
"column": 47
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\nx : M\n⊢ ¬I.IsBoundaryPoint x → I.IsIn... | [
"𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\nx : M\n⊢ ¬I.IsBoundaryPoint x → I.IsInteriorPoint ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.MongePoint | {
"line": 690,
"column": 70
} | {
"line": 690,
"column": 81
} | {
"line": 690,
"column": 82
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Set P\nt t₀ : Triangle ℝ P\nht : Set.range t.points ⊆ insert t₀.orthocenter (Set.range t₀.points)\nht₀o : t₀.orthocenter ∉ Set.range t₀.points\nht₀s : s = ... | [
"V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Set P\nt t₀ : Triangle ℝ P\nht : Set.range t.points ⊆ insert t₀.orthocenter (Set.range t₀.points)\nht₀o : t₀.orthocenter ∉ Set.range t₀.points\nht₀s : s = insert t₀.or... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.MongePoint | {
"line": 691,
"column": 70
} | {
"line": 691,
"column": 81
} | {
"line": 691,
"column": 82
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Set P\nt t₀ : Triangle ℝ P\nht : Set.range t.points ⊆ insert t₀.orthocenter (Set.range t₀.points)\nht₀o : t₀.orthocenter ∉ Set.range t₀.points\nht₀s : s = ... | [
"V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Set P\nt t₀ : Triangle ℝ P\nht : Set.range t.points ⊆ insert t₀.orthocenter (Set.range t₀.points)\nht₀o : t₀.orthocenter ∉ Set.range t₀.points\nht₀s : s = insert t₀.or... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Complex | {
"line": 133,
"column": 4
} | {
"line": 133,
"column": 29
} | {
"line": 133,
"column": 30
} | [
{
"pp": "case inr\nE : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℂ E\nF : Type u_2\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace ℂ F\nH : Type u_3\ninst✝⁴ : TopologicalSpace H\nI : ModelWithCorners ℂ E H\ninst✝³ : I.Boundaryless\nM : Type u_4\ninst✝² : TopologicalSpace M\ninst✝¹ : Cha... | [
"case inr\nE : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℂ E\nF : Type u_2\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace ℂ F\nH : Type u_3\ninst✝⁴ : TopologicalSpace H\nI : ModelWithCorners ℂ E H\ninst✝³ : I.Boundaryless\nM : Type u_4\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 413,
"column": 2
} | {
"line": 413,
"column": 13
} | {
"line": 413,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁷ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁶ : TopologicalSpace M\ninst✝⁵ : ChartedSpace H M\nE' : Type u_5\ninst✝⁴ : NormedAddCom... | [
"𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁷ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁶ : TopologicalSpace M\ninst✝⁵ : ChartedSpace H M\nE' : Type u_5\ninst✝⁴ : NormedAddCommGroup E'\ni... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 417,
"column": 2
} | {
"line": 417,
"column": 13
} | {
"line": 417,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁷ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁶ : TopologicalSpace M\ninst✝⁵ : ChartedSpace H M\nE' : Type u_5\ninst✝⁴ : NormedAddCom... | [
"𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁷ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁶ : TopologicalSpace M\ninst✝⁵ : ChartedSpace H M\nE' : Type u_5\ninst✝⁴ : NormedAddCommGroup E'\ni... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 467,
"column": 2
} | {
"line": 467,
"column": 70
} | {
"line": 468,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\nu : Opens M\nx : ↥u\n⊢ I.IsBoundaryPoi... | [
"𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\nu : Opens M\nx : ↥u\n⊢ I.IsBoundaryPoint x ↔ I.IsB... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.Tangent | {
"line": 93,
"column": 6
} | {
"line": 93,
"column": 17
} | {
"line": 93,
"column": 18
} | [
{
"pp": "case e_f.e_f.hc\n𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁸ : TopologicalSpace M\ninst✝⁷ : ChartedSpace H M\ninst✝⁶ : IsManifo... | [
"case e_f.e_f.hc\n𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁸ : TopologicalSpace M\ninst✝⁷ : ChartedSpace H M\ninst✝⁶ : IsManifold I 1 M\nE'... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 557,
"column": 2
} | {
"line": 557,
"column": 49
} | {
"line": 557,
"column": 50
} | [
{
"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\nM' : Type u_5\ninst✝¹ : TopologicalSp... | [
"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\nM' : Type u_5\ninst✝¹ : TopologicalSpace M'\ninst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 564,
"column": 2
} | {
"line": 564,
"column": 49
} | {
"line": 564,
"column": 50
} | [
{
"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\nM' : Type u_5\ninst✝¹ : TopologicalSp... | [
"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\nM' : Type u_5\ninst✝¹ : TopologicalSpace M'\ninst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 571,
"column": 2
} | {
"line": 571,
"column": 49
} | {
"line": 571,
"column": 50
} | [
{
"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\nM' : Type u_5\ninst✝¹ : TopologicalSp... | [
"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\nM' : Type u_5\ninst✝¹ : TopologicalSpace M'\ninst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 578,
"column": 2
} | {
"line": 578,
"column": 49
} | {
"line": 578,
"column": 50
} | [
{
"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\nM' : Type u_5\ninst✝¹ : TopologicalSp... | [
"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\nM' : Type u_5\ninst✝¹ : TopologicalSpace M'\ninst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 606,
"column": 2
} | {
"line": 606,
"column": 55
} | {
"line": 607,
"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\nM' : Type u_5\ninst✝¹ : TopologicalSp... | [
"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\nM' : Type u_5\ninst✝¹ : TopologicalSpace M'\ninst... | rw [← Boundaryless.iff_boundary_eq_empty] at hM hM' ⊢ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable | {
"line": 67,
"column": 2
} | {
"line": 67,
"column": 46
} | {
"line": 67,
"column": 47
} | [
{
"pp": "𝕜 : Type u_1\nB : Type u_2\nF : Type u_4\nM : Type u_5\nE : B → Type u_6\ninst✝¹⁵ : NontriviallyNormedField 𝕜\ninst✝¹⁴ : NormedAddCommGroup F\ninst✝¹³ : NormedSpace 𝕜 F\ninst✝¹² : TopologicalSpace (TotalSpace F E)\ninst✝¹¹ : (x : B) → TopologicalSpace (E x)\nEB : Type u_7\ninst✝¹⁰ : NormedAddCommGro... | [
"𝕜 : Type u_1\nB : Type u_2\nF : Type u_4\nM : Type u_5\nE : B → Type u_6\ninst✝¹⁵ : NontriviallyNormedField 𝕜\ninst✝¹⁴ : NormedAddCommGroup F\ninst✝¹³ : NormedSpace 𝕜 F\ninst✝¹² : TopologicalSpace (TotalSpace F E)\ninst✝¹¹ : (x : B) → TopologicalSpace (E x)\nEB : Type u_7\ninst✝¹⁰ : NormedAddCommGroup EB\ninst✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable | {
"line": 81,
"column": 2
} | {
"line": 81,
"column": 46
} | {
"line": 81,
"column": 47
} | [
{
"pp": "𝕜 : Type u_1\nB : Type u_2\nF : Type u_4\nE : B → Type u_6\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedAddCommGroup F\ninst✝⁸ : NormedSpace 𝕜 F\ninst✝⁷ : TopologicalSpace (TotalSpace F E)\ninst✝⁶ : (x : B) → TopologicalSpace (E x)\nEB : Type u_7\ninst✝⁵ : NormedAddCommGroup EB\ninst✝⁴ : Nor... | [
"𝕜 : Type u_1\nB : Type u_2\nF : Type u_4\nE : B → Type u_6\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedAddCommGroup F\ninst✝⁸ : NormedSpace 𝕜 F\ninst✝⁷ : TopologicalSpace (TotalSpace F E)\ninst✝⁶ : (x : B) → TopologicalSpace (E x)\nEB : Type u_7\ninst✝⁵ : NormedAddCommGroup EB\ninst✝⁴ : NormedSpace 𝕜 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable | {
"line": 258,
"column": 2
} | {
"line": 258,
"column": 46
} | {
"line": 259,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\nB : Type u_2\nF : Type u_4\nM : Type u_5\nE : B → Type u_6\ninst✝²¹ : NontriviallyNormedField 𝕜\ninst✝²⁰ : NormedAddCommGroup F\ninst✝¹⁹ : NormedSpace 𝕜 F\ninst✝¹⁸ : TopologicalSpace (TotalSpace F E)\ninst✝¹⁷ : (x : B) → TopologicalSpace (E x)\nEB : Type u_7\ninst✝¹⁶ : NormedAddCommGro... | [
"𝕜 : Type u_1\nB : Type u_2\nF : Type u_4\nM : Type u_5\nE : B → Type u_6\ninst✝²¹ : NontriviallyNormedField 𝕜\ninst✝²⁰ : NormedAddCommGroup F\ninst✝¹⁹ : NormedSpace 𝕜 F\ninst✝¹⁸ : TopologicalSpace (TotalSpace F E)\ninst✝¹⁷ : (x : B) → TopologicalSpace (E x)\nEB : Type u_7\ninst✝¹⁶ : NormedAddCommGroup EB\ninst✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable | {
"line": 307,
"column": 2
} | {
"line": 307,
"column": 46
} | {
"line": 307,
"column": 47
} | [
{
"pp": "𝕜 : Type u_1\nB : Type u_2\nF : Type u_4\nE : B → Type u_6\ninst✝¹⁵ : NontriviallyNormedField 𝕜\ninst✝¹⁴ : NormedAddCommGroup F\ninst✝¹³ : NormedSpace 𝕜 F\ninst✝¹² : TopologicalSpace (TotalSpace F E)\ninst✝¹¹ : (x : B) → TopologicalSpace (E x)\nEB : Type u_7\ninst✝¹⁰ : NormedAddCommGroup EB\ninst✝⁹ ... | [
"𝕜 : Type u_1\nB : Type u_2\nF : Type u_4\nE : B → Type u_6\ninst✝¹⁵ : NontriviallyNormedField 𝕜\ninst✝¹⁴ : NormedAddCommGroup F\ninst✝¹³ : NormedSpace 𝕜 F\ninst✝¹² : TopologicalSpace (TotalSpace F E)\ninst✝¹¹ : (x : B) → TopologicalSpace (E x)\nEB : Type u_7\ninst✝¹⁰ : NormedAddCommGroup EB\ninst✝⁹ : NormedSpac... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable | {
"line": 489,
"column": 4
} | {
"line": 489,
"column": 38
} | {
"line": 489,
"column": 39
} | [
{
"pp": "case insert\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 : Fiber... | [
"case insert\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\n... | 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.VectorBundle.MDifferentiable | {
"line": 585,
"column": 4
} | {
"line": 585,
"column": 15
} | {
"line": 585,
"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": 664,
"column": 6
} | {
"line": 664,
"column": 29
} | {
"line": 664,
"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.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.VectorBundle.MDifferentiable | {
"line": 748,
"column": 2
} | {
"line": 748,
"column": 13
} | {
"line": 748,
"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.MDifferentiable | {
"line": 758,
"column": 2
} | {
"line": 758,
"column": 13
} | {
"line": 758,
"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.NormedSpace | {
"line": 114,
"column": 2
} | {
"line": 114,
"column": 34
} | {
"line": 114,
"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": 122,
"column": 2
} | {
"line": 122,
"column": 34
} | {
"line": 122,
"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": 405,
"column": 2
} | {
"line": 405,
"column": 13
} | {
"line": 405,
"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": 553,
"column": 2
} | {
"line": 553,
"column": 13
} | {
"line": 553,
"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": 595,
"column": 2
} | {
"line": 595,
"column": 13
} | {
"line": 595,
"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.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": 350,
"column": 2
} | {
"line": 350,
"column": 13
} | {
"line": 350,
"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.VectorField.Pullback | {
"line": 559,
"column": 2
} | {
"line": 559,
"column": 13
} | {
"line": 559,
"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": 608,
"column": 2
} | {
"line": 608,
"column": 13
} | {
"line": 608,
"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": 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.Instances.Real | {
"line": 153,
"column": 2
} | {
"line": 153,
"column": 53
} | {
"line": 153,
"column": 54
} | [
{
"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",
"Set.ofPred",
"PartialO... | [
"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": 372,
"column": 2
} | {
"line": 372,
"column": 81
} | {
"line": 373,
"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": 373,
"column": 30
} | {
"line": 373,
"column": 41
} | {
"line": 373,
"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": 373,
"column": 74
} | {
"line": 373,
"column": 85
} | {
"line": 373,
"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.Immersion | {
"line": 446,
"column": 38
} | {
"line": 446,
"column": 73
} | {
"line": 446,
"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.Instances.Real | {
"line": 427,
"column": 6
} | {
"line": 427,
"column": 31
} | {
"line": 427,
"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": 582,
"column": 80
} | {
"line": 582,
"column": 91
} | {
"line": 582,
"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.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.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.Instances.Icc | {
"line": 189,
"column": 2
} | {
"line": 189,
"column": 35
} | {
"line": 190,
"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.VectorField.LieBracket | {
"line": 592,
"column": 6
} | {
"line": 592,
"column": 83
} | {
"line": 593,
"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.VectorField.LieBracket | {
"line": 592,
"column": 6
} | {
"line": 592,
"column": 83
} | {
"line": 593,
"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": 592,
"column": 6
} | {
"line": 592,
"column": 83
} | {
"line": 593,
"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.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.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.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": 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.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": 460,
"column": 31
} | {
"line": 460,
"column": 42
} | {
"line": 460,
"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.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.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.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.Instances.Sphere | {
"line": 536,
"column": 78
} | {
"line": 539,
"column": 37
} | {
"line": 540,
"column": 2
} | [
{
"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 : Injective ⇑(fderiv ℝ ((stereoInvFunAux (-↑v) ∘ ... | [] | by
convert! this using 3
congr 2
apply stereographic'_neg (v := v) | [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.Sphere | {
"line": 550,
"column": 2
} | {
"line": 550,
"column": 38
} | {
"line": 550,
"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": 624,
"column": 2
} | {
"line": 624,
"column": 15
} | {
"line": 625,
"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": 630,
"column": 6
} | {
"line": 631,
"column": 26
} | {
"line": 632,
"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": 630,
"column": 6
} | {
"line": 631,
"column": 26
} | {
"line": 632,
"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": 630,
"column": 6
} | {
"line": 631,
"column": 26
} | {
"line": 632,
"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.Metrizable | {
"line": 33,
"column": 2
} | {
"line": 33,
"column": 58
} | {
"line": 34,
"column": 2
} | [
{
"pp": "E : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : FiniteDimensional 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 : SigmaCompactSpace M\ninst✝ : T2Space M\nthis✝¹ : L... | [
"E : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : FiniteDimensional 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 : SigmaCompactSpace M\ninst✝ : T2Space M\nthis✝² : LocallyCompac... | have := ChartedSpace.secondCountable_of_sigmaCompact H M | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
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 |
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