module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.Topology.MetricSpace.Similarity | {
"line": 67,
"column": 34
} | {
"line": 67,
"column": 45
} | [
{
"pp": "ι : Type u_1\nP₁ : Type u_3\nP₂ : Type u_4\ninst✝¹ : PseudoEMetricSpace P₁\ninst✝ : PseudoEMetricSpace P₂\nv₁ : ι → P₁\nv₂ : ι → P₂\nh : v₁ ≅ v₂\ni₁ i₂ : ι\n⊢ edist (v₁ i₁) (v₁ i₂) = ↑1 * edist (v₂ i₁) (v₂ i₂)",
"usedConstants": [
"Eq.mpr",
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.Similarity | {
"line": 115,
"column": 2
} | {
"line": 115,
"column": 46
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.NinePointCircle | {
"line": 72,
"column": 23
} | {
"line": 72,
"column": 34
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.NinePointCircle | {
"line": 102,
"column": 28
} | {
"line": 102,
"column": 39
} | [
{
"pp": "V : 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\ni : Fin (n + 1)\n⊢ ↑n ≠ 0",
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.NinePointCircle | {
"line": 105,
"column": 26
} | {
"line": 105,
"column": 37
} | [
{
"pp": "V : 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\ni : Fin (n + 1)\n⊢ ↑n ≠ 0",
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.NinePointCircle | {
"line": 112,
"column": 4
} | {
"line": 112,
"column": 15
} | [
{
"pp": "case a.left\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⊢ s.ninePointCircle.center ∈ affineSpan ℝ (Set.range s.medial.points)",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.NinePointCircle | {
"line": 114,
"column": 4
} | {
"line": 114,
"column": 31
} | [
{
"pp": "case a.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.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.NinePointCircle | {
"line": 126,
"column": 23
} | {
"line": 126,
"column": 34
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.NinePointCircle | {
"line": 157,
"column": 30
} | {
"line": 157,
"column": 41
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"Real",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.NinePointCircle | {
"line": 181,
"column": 55
} | {
"line": 181,
"column": 80
} | [
{
"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",
"usedConstants": [
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.NinePointCircle | {
"line": 187,
"column": 50
} | {
"line": 187,
"column": 61
} | [
{
"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",
"usedConstants": [
"Eq.m... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.MongePoint | {
"line": 92,
"column": 27
} | {
"line": 92,
"column": 38
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.Power | {
"line": 188,
"column": 4
} | {
"line": 188,
"column": 54
} | [
{
"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 :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.MongePoint | {
"line": 279,
"column": 27
} | {
"line": 279,
"column": 38
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.Power | {
"line": 197,
"column": 4
} | {
"line": 197,
"column": 58
} | [
{
"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 :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Group.Growth.LinearLowerBound | {
"line": 30,
"column": 4
} | {
"line": 31,
"column": 11
} | [
{
"pp": "case inl\nG : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nX : Finset G\nhX₁ : 1 ∈ X\nhX : X.Nontrivial\nhXclosure : ↑X ^ 0 ≠ ↑(closure ↑X)\n⊢ X ^ 0 ⊂ X ^ (0 + 1)",
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"_private.Mathlib.Geometry.Group.Growth.LinearLowerBound.0.Finset... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Group.Growth.LinearLowerBound | {
"line": 51,
"column": 6
} | {
"line": 51,
"column": 31
} | [
{
"pp": "G✝ : Type u_1\ninst✝³ : Group G✝\ninst✝² : DecidableEq G✝\nX✝ : Finset G✝\nn : ℕ\nG : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nX : Finset G\nhX₁ : 1 ∈ X\nhX : X.Nontrivial\nhn : True\nhXn : X = X ^ 2\nx y : G\nhx : x ∈ X\nhy : y ∈ X\n⊢ x * y ∈ X",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Group.Growth.LinearLowerBound | {
"line": 56,
"column": 8
} | {
"line": 56,
"column": 44
} | [
{
"pp": "G✝ : Type u_1\ninst✝³ : Group G✝\ninst✝² : DecidableEq G✝\nX✝ : Finset G✝\nn : ℕ\nG : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nX : Finset G\nhX₁ : 1 ∈ X\nhX : X.Nontrivial\nhn : True\nhXn : X = X ^ 2\nx : G\nhx : x ∈ X\n⊢ x • X ⊆ X",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Group.Growth.LinearLowerBound | {
"line": 74,
"column": 40
} | {
"line": 74,
"column": 68
} | [
{
"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)",
"usedConstants": [
"Eq.mp... | 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
} | [
{
"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)",
"usedConstants": [
"Eq.mp... | rw [← pow_add]; congr 1; lia | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Group.Growth.LinearLowerBound | {
"line": 84,
"column": 2
} | {
"line": 84,
"column": 17
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Group.Growth.QuotientInter | {
"line": 35,
"column": 29
} | {
"line": 35,
"column": 40
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Group.Growth.QuotientInter | {
"line": 37,
"column": 4
} | {
"line": 37,
"column": 15
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Group.Growth.QuotientInter | {
"line": 38,
"column": 72
} | {
"line": 38,
"column": 83
} | [
{
"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 →... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Group.Growth.QuotientInter | {
"line": 52,
"column": 8
} | {
"line": 52,
"column": 71
} | [
{
"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 →... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 206,
"column": 8
} | {
"line": 206,
"column": 19
} | [
{
"pp": "X : Type u_2\ninst✝ : EMetricSpace X\nμ : OuterMeasure X\nhm : μ.IsMetric\nt : Set X\nht : t ∈ {s | IsClosed[PseudoEMetricSpace.toUniformSpace.toTopologicalSpace] s}\ns : Set X\nS : ℕ → Set X := fun n ↦ {x | x ∈ s ∧ (↑n)⁻¹ ≤ infEDist x t}\nSsep : ∀ (n : ℕ), AreSeparated (S n) t\nSsep' : ∀ (n : ℕ), AreS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 206,
"column": 31
} | {
"line": 206,
"column": 42
} | [
{
"pp": "X : Type u_2\ninst✝ : EMetricSpace X\nμ : OuterMeasure X\nhm : μ.IsMetric\nt : Set X\nht : t ∈ {s | IsClosed[PseudoEMetricSpace.toUniformSpace.toTopologicalSpace] s}\ns : Set X\nS : ℕ → Set X := fun n ↦ {x | x ∈ s ∧ (↑n)⁻¹ ≤ infEDist x t}\nSsep : ∀ (n : ℕ), AreSeparated (S n) t\nSsep' : ∀ (n : ℕ), AreS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.MongePoint | {
"line": 689,
"column": 70
} | {
"line": 689,
"column": 81
} | [
{
"pp": "case h\nV : 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\nht₀... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.MongePoint | {
"line": 690,
"column": 70
} | {
"line": 690,
"column": 81
} | [
{
"pp": "case h\nV : 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\nht₀... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 219,
"column": 54
} | {
"line": 219,
"column": 87
} | [
{
"pp": "X : Type u_2\ninst✝ : EMetricSpace X\nμ : OuterMeasure X\nhm : μ.IsMetric\nt : Set X\nht : t ∈ {s | IsClosed[PseudoEMetricSpace.toUniformSpace.toTopologicalSpace] s}\ns : Set X\nS : ℕ → Set X := fun n ↦ {x | x ∈ s ∧ (↑n)⁻¹ ≤ infEDist x t}\nSsep : ∀ (n : ℕ), AreSeparated (S n) t\nSsep' : ∀ (n : ℕ), AreS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 344,
"column": 2
} | {
"line": 344,
"column": 13
} | [
{
"pp": "X : Type u_2\ninst✝ : EMetricSpace X\nb : OuterMeasure X\nhb : ∀ (i : ℝ≥0∞), ⨆ (_ : i > 0), ⊤ ≤ b\n⊢ ⊤ ≤ b",
"usedConstants": [
"Eq.mpr",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CompleteLattice.toBoundedOrder",
"MeasureTheory.OuterMeasure",
"id",
"LE.l... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 528,
"column": 2
} | {
"line": 528,
"column": 33
} | [
{
"pp": "X : Type u_2\ninst✝² : EMetricSpace X\ninst✝¹ : MeasurableSpace X\ninst✝ : BorelSpace X\nβ : Type u_4\nι : β → Type u_5\nhι : (n : β) → Fintype (ι n)\ns : Set X\nl : Filter β\nr : β → ℝ≥0∞\nhr : Tendsto r l (𝓝 0)\nt : (n : β) → ι n → Set X\nht : ∀ᶠ (n : β) in l, ∀ (i : ι n), ediam (t n i) ≤ r n\nhst :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 593,
"column": 32
} | {
"line": 593,
"column": 74
} | [
{
"pp": "X : Type u_2\ninst✝² : EMetricSpace X\ninst✝¹ : MeasurableSpace X\ninst✝ : BorelSpace X\nd₁ d₂ : ℝ\nh : d₁ < d₂\ns : Set X\nH : μH[d₂] s ≠ 0 ∧ μH[d₁] s ≠ ∞\nc : ℝ≥0\nhc : c ≠ 0\nthis : 0 < ↑c ^ (d₂ - d₁)⁻¹\nr : ℝ≥0\nhr₀✝ : 0 ≤ ↑r\nhrc : ↑r < ↑c ^ (d₂ - d₁)⁻¹\nhr₀ : r ≠ 0\n⊢ ↑r ≠ 0",
"usedConstants"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Volume.Measure | {
"line": 52,
"column": 2
} | {
"line": 52,
"column": 13
} | [
{
"pp": "d : ℕ\n⊢ μH[↑d].IsAddHaarMeasure",
"usedConstants": [
"Real",
"fact_one_le_two_ennreal",
"MeasureTheory.Measure.hausdorffMeasure",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"WithLp.instAddCommGroup",
"PiLp.instEMetricSpace",
"id",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Volume.Measure | {
"line": 97,
"column": 2
} | {
"line": 97,
"column": 41
} | [
{
"pp": "X : Type u_1\ninst✝² : EMetricSpace X\ninst✝¹ : MeasurableSpace X\ninst✝ : BorelSpace X\nbasis : OrthonormalBasis (Fin 0) ℝ (EuclideanSpace ℝ (Fin 0)) := EuclideanSpace.basisFun (Fin 0) ℝ\nheq : {0} = parallelepiped ⇑basis\nh✝ : volume = volume.addHaarScalarFactor μH[↑0] • μH[↑0]\nh : volume.addHaarSca... | simp [euclideanHausdorffMeasure_def, h] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Geometry.Euclidean.Volume.Measure | {
"line": 113,
"column": 8
} | {
"line": 113,
"column": 19
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝¹⁰ : EMetricSpace X\ninst✝⁹ : MeasurableSpace X\ninst✝⁸ : BorelSpace X\ninst✝⁷ : EMetricSpace Y\ninst✝⁶ : MeasurableSpace Y\ninst✝⁵ : BorelSpace Y\nE : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : FiniteDimensional ℝ E\ninst✝¹ : Measurable... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Volume.Measure | {
"line": 121,
"column": 70
} | {
"line": 121,
"column": 81
} | [
{
"pp": "X : Type u_1\ninst✝² : EMetricSpace X\ninst✝¹ : MeasurableSpace X\ninst✝ : BorelSpace X\nd₁ d₂ : ℕ\nh : d₁ < d₂\ns : Set X\n⊢ ↑d₁ < ↑d₂",
"usedConstants": [
"Eq.mpr",
"Real.partialOrder",
"Real",
"Real.instRCLike",
"Real.instZeroLEOneClass",
"Nat.cast_lt._simp_1"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 620,
"column": 4
} | {
"line": 620,
"column": 33
} | [
{
"pp": "case a\nX : Type u_2\ninst✝² : EMetricSpace X\ninst✝¹ : MeasurableSpace X\ninst✝ : BorelSpace X\nx : X\nr : ℕ → ℝ≥0∞ := fun x ↦ 0\nt : ℕ → Unit → Set X := fun x_1 x_2 ↦ {x}\nht : ∀ᶠ (n : ℕ) in atTop, ∀ (i : Unit), ediam (t n i) ≤ r n\n⊢ μH[0] {x} ≤ 1",
"usedConstants": [
"Eq.mpr",
"Real... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 681,
"column": 41
} | {
"line": 681,
"column": 72
} | [
{
"pp": "X : Type u_2\nY : Type u_3\ninst✝⁵ : EMetricSpace X\ninst✝⁴ : EMetricSpace Y\ninst✝³ : MeasurableSpace X\ninst✝² : BorelSpace X\ninst✝¹ : MeasurableSpace Y\ninst✝ : BorelSpace Y\nr : ℝ≥0\nf : X → Y\ns : Set X\nhr : 0 < r\nd : ℝ\nhd : 0 ≤ d\nh : HolderOnWith 0 r f s\nx : X\nhx : x ∈ s\n⊢ (f '' s).Subsin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Volume.Measure | {
"line": 294,
"column": 12
} | {
"line": 294,
"column": 23
} | [
{
"pp": "V : Type u_3\nP : Type u_4\ninst✝⁸ : NormedAddCommGroup V\ninst✝⁷ : InnerProductSpace ℝ V\ninst✝⁶ : MeasurableSpace V\ninst✝⁵ : BorelSpace V\ninst✝⁴ : FiniteDimensional ℝ V\ninst✝³ : MetricSpace P\ninst✝² : MeasurableSpace P\ninst✝¹ : BorelSpace P\ninst✝ : NormedAddTorsor V P\ns : AffineSubspace ℝ P\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Volume.Measure | {
"line": 349,
"column": 48
} | {
"line": 349,
"column": 64
} | [
{
"pp": "V : Type u_3\nP : Type u_4\ninst✝⁸ : NormedAddCommGroup V\ninst✝⁷ : InnerProductSpace ℝ V\ninst✝⁶ : MeasurableSpace V\ninst✝⁵ : BorelSpace V\ninst✝⁴ : FiniteDimensional ℝ V\ninst✝³ : MetricSpace P\ninst✝² : MeasurableSpace P\ninst✝¹ : BorelSpace P\ninst✝ : NormedAddTorsor V P\np : P\nv : V\nhv : v ≠ 0\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 723,
"column": 2
} | {
"line": 723,
"column": 44
} | [
{
"pp": "X : Type u_2\nY : Type u_3\ninst✝⁵ : EMetricSpace X\ninst✝⁴ : EMetricSpace Y\ninst✝³ : MeasurableSpace X\ninst✝² : BorelSpace X\ninst✝¹ : MeasurableSpace Y\ninst✝ : BorelSpace Y\nK : ℝ≥0\nf : X → Y\ns : Set X\nh : LipschitzOnWith K f s\nd : ℝ\nhd : 0 ≤ d\n⊢ μH[d] (f '' s) ≤ ↑K ^ d * μH[d] s",
"used... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 746,
"column": 4
} | {
"line": 747,
"column": 11
} | [
{
"pp": "𝕜 : Type u_4\nE : Type u_5\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedDivisionRing 𝕜\ninst✝³ : Module 𝕜 E\ninst✝² : NormSMulClass 𝕜 E\ninst✝¹ : MeasurableSpace E\ninst✝ : BorelSpace E\nd : ℝ\nhd : 0 ≤ d\nr✝ : 𝕜\nhr : r✝ ≠ 0\ns✝ : Set E\nr : 𝕜\ns : Set E\n⊢ μH[d] (r • s) ≤ ‖r‖₊ ^ d • μH[d] s",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 900,
"column": 4
} | {
"line": 900,
"column": 46
} | [
{
"pp": "ι : Type u_4\ninst✝ : Fintype ι\na b : ι → ℚ\nH : ∀ (i : ι), a i < b i\ni : ι\n⊢ 0 ≤ ↑(b i) - ↑(a i)",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Real.instLE",
"Real",
"Real.instZero",
"Real.instSub",
"covariant_swap_add_of_covariant_add"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 924,
"column": 10
} | {
"line": 924,
"column": 49
} | [
{
"pp": "case h'\nι : Type u_4\ninst✝ : Fintype ι\na b : ι → ℚ\nH : ∀ (i : ι), a i < b i\nI : ∀ (i : ι), 0 ≤ ↑(b i) - ↑(a i)\nγ : ℕ → Type u_4 := fun n ↦ (i : ι) → Fin ⌈(↑(b i) - ↑(a i)) * ↑n⌉₊\nt : (n : ℕ) → γ n → Set (ι → ℝ) := fun n f ↦ univ.pi fun i ↦ Icc (↑(a i) + ↑↑(f i) / ↑n) (↑(a i) + (↑↑(f i) + 1) / ↑n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.Tangent | {
"line": 64,
"column": 55
} | {
"line": 64,
"column": 79
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nn : ℕ∞ω\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_4\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_6\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\ninst✝ : IsManifold I (n + 1)... | apply image_subset_range | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 943,
"column": 8
} | {
"line": 947,
"column": 39
} | [
{
"pp": "case refine_1\nι : Type u_4\ninst✝ : Fintype ι\na b : ι → ℚ\nH : ∀ (i : ι), a i < b i\nI : ∀ (i : ι), 0 ≤ ↑(b i) - ↑(a i)\nγ : ℕ → Type u_4 := fun n ↦ (i : ι) → Fin ⌈(↑(b i) - ↑(a i)) * ↑n⌉₊\nt : (n : ℕ) → γ n → Set (ι → ℝ) := fun n f ↦ univ.pi fun i ↦ Icc (↑(a i) + ↑↑(f i) / ↑n) (↑(a i) + (↑↑(f i) + 1... | filter_upwards [B] with _ hn
apply Finset.sum_le_sum fun i _ => _
simp only [ENNReal.rpow_natCast]
intro i _
exact pow_le_pow_left' (hn i) _ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 943,
"column": 8
} | {
"line": 947,
"column": 39
} | [
{
"pp": "case refine_1\nι : Type u_4\ninst✝ : Fintype ι\na b : ι → ℚ\nH : ∀ (i : ι), a i < b i\nI : ∀ (i : ι), 0 ≤ ↑(b i) - ↑(a i)\nγ : ℕ → Type u_4 := fun n ↦ (i : ι) → Fin ⌈(↑(b i) - ↑(a i)) * ↑n⌉₊\nt : (n : ℕ) → γ n → Set (ι → ℝ) := fun n f ↦ univ.pi fun i ↦ Icc (↑(a i) + ↑↑(f i) / ↑n) (↑(a i) + (↑↑(f i) + 1... | filter_upwards [B] with _ hn
apply Finset.sum_le_sum fun i _ => _
simp only [ENNReal.rpow_natCast]
intro i _
exact pow_le_pow_left' (hn i) _ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 1034,
"column": 4
} | {
"line": 1035,
"column": 44
} | [
{
"pp": "E : Type u_5\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : MeasurableSpace E\ninst✝ : BorelSpace E\nv : E\ns : Set ℝ\nhv : v ≠ 0\nhn : ‖v‖ ≠ 0\nthis : μH[1] ((fun x ↦ ‖v‖ • x) '' ⇑(LinearMap.toSpanSingleton ℝ E (‖v‖⁻¹ • v)) '' s) = ‖v‖₊ • μH[1] s\n⊢ μH[1] ((fun r ↦ r • v) '' s) = ‖... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.Tangent | {
"line": 290,
"column": 2
} | {
"line": 290,
"column": 62
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_8\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nb b' x : F\n⊢ (tangentBundleCore 𝓘(𝕜, F) F).coordChange (achart F b) (achart F b') x = 1",
"usedConstants": [
"Eq.mpr",
"chartedSpaceSelf",
"ENat.instNatCas... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 1112,
"column": 2
} | {
"line": 1112,
"column": 13
} | [
{
"pp": "𝕜 : Type u_4\nE : Type u_5\ninst✝⁵ : RCLike 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\nK : Submodule 𝕜 E\ninst✝ : K.HasOrthogonalProjection\nd : ℝ\ns : Set E\nhs : 0 ≤ d\n⊢ μH[d] (⇑K.orthogonalProjection '' s) ≤ μH[d] s",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.Tangent | {
"line": 406,
"column": 6
} | {
"line": 406,
"column": 35
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁴ : NontriviallyNormedField 𝕜\nn : ℕ∞ω\nE : Type u_2\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedSpace 𝕜 E\nE' : Type u_3\ninst✝¹¹ : NormedAddCommGroup E'\ninst✝¹⁰ : NormedSpace 𝕜 E'\nH : Type u_4\ninst✝⁹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nH' : Type u_5\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.Tangent | {
"line": 413,
"column": 6
} | {
"line": 413,
"column": 35
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁴ : NontriviallyNormedField 𝕜\nn : ℕ∞ω\nE : Type u_2\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedSpace 𝕜 E\nE' : Type u_3\ninst✝¹¹ : NormedAddCommGroup E'\ninst✝¹⁰ : NormedSpace 𝕜 E'\nH : Type u_4\ninst✝⁹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nH' : Type u_5\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.Tangent | {
"line": 447,
"column": 2
} | {
"line": 447,
"column": 33
} | [
{
"pp": "𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nn : ℕ∞ω\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\nH : Type u_4\ninst✝ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nx✝ : ModelProd H E\ny : TangentBundle I H\nb : E\nx : H\n⊢ ↑I\n ({ toFun := fun x ↦ (x.proj,... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.Atlas | {
"line": 377,
"column": 4
} | {
"line": 377,
"column": 15
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\ninst✝ : IsManifold I 1 M\nx₀ x : M\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.Atlas | {
"line": 399,
"column": 2
} | {
"line": 399,
"column": 13
} | [
{
"pp": "case h\n𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\ninst✝ : IsManifold I 1 M\nx :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.Atlas | {
"line": 411,
"column": 2
} | {
"line": 411,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\ninst✝ : IsManifold I 1 M\nx : M\nhcom... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 138,
"column": 7
} | {
"line": 138,
"column": 46
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 365,
"column": 4
} | {
"line": 365,
"column": 45
} | [
{
"pp": "𝕜✝ : Type u_1\ninst✝²¹ : NontriviallyNormedField 𝕜✝\nE✝ : Type u_2\ninst✝²⁰ : NormedAddCommGroup E✝\ninst✝¹⁹ : NormedSpace 𝕜✝ E✝\nH✝ : Type u_3\ninst✝¹⁸ : TopologicalSpace H✝\nI✝ : ModelWithCorners 𝕜✝ E✝ H✝\nM✝ : Type u_4\ninst✝¹⁷ : TopologicalSpace M✝\ninst✝¹⁶ : ChartedSpace H✝ M✝\nE'✝ : Type u_5\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Diffeomorph | {
"line": 291,
"column": 4
} | {
"line": 291,
"column": 60
} | [
{
"pp": "case mp\n𝕜 : Type u_1\ninst✝¹⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹⁴ : NormedAddCommGroup E\ninst✝¹³ : NormedSpace 𝕜 E\nE' : Type u_3\ninst✝¹² : NormedAddCommGroup E'\ninst✝¹¹ : NormedSpace 𝕜 E'\nF : Type u_4\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NormedSpace 𝕜 F\nH : Type u_5\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Diffeomorph | {
"line": 317,
"column": 4
} | {
"line": 317,
"column": 60
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹⁴ : NormedAddCommGroup E\ninst✝¹³ : NormedSpace 𝕜 E\nE' : Type u_3\ninst✝¹² : NormedAddCommGroup E'\ninst✝¹¹ : NormedSpace 𝕜 E'\nF : Type u_4\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NormedSpace 𝕜 F\nH : Type u_5\ninst✝⁸ : Top... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 378,
"column": 4
} | {
"line": 378,
"column": 15
} | [
{
"pp": "case refine_4\n𝕜✝ : Type u_1\ninst✝²¹ : NontriviallyNormedField 𝕜✝\nE✝ : Type u_2\ninst✝²⁰ : NormedAddCommGroup E✝\ninst✝¹⁹ : NormedSpace 𝕜✝ E✝\nH✝ : Type u_3\ninst✝¹⁸ : TopologicalSpace H✝\nI✝ : ModelWithCorners 𝕜✝ E✝ H✝\nM✝ : Type u_4\ninst✝¹⁷ : TopologicalSpace M✝\ninst✝¹⁶ : ChartedSpace H✝ M✝\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Diffeomorph | {
"line": 418,
"column": 4
} | {
"line": 418,
"column": 15
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹⁷ : NormedAddCommGroup E\ninst✝¹⁶ : NormedSpace 𝕜 E\nE' : Type u_3\ninst✝¹⁵ : NormedAddCommGroup E'\ninst✝¹⁴ : NormedSpace 𝕜 E'\nF : Type u_4\ninst✝¹³ : NormedAddCommGroup F\ninst✝¹² : NormedSpace 𝕜 F\nH : Type u_5\ninst✝¹¹ : T... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 402,
"column": 2
} | {
"line": 402,
"column": 13
} | [
{
"pp": "case h\n𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁷ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁶ : TopologicalSpace M\ninst✝⁵ : ChartedSpace H M\nE' : Type u_5\ninst✝⁴ : Norm... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 407,
"column": 2
} | {
"line": 407,
"column": 13
} | [
{
"pp": "case h\n𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁷ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁶ : TopologicalSpace M\ninst✝⁵ : ChartedSpace H M\nE' : Type u_5\ninst✝⁴ : Norm... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 411,
"column": 2
} | {
"line": 411,
"column": 13
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 415,
"column": 2
} | {
"line": 415,
"column": 13
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 458,
"column": 2
} | {
"line": 459,
"column": 72
} | [
{
"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.IsInteriorPoi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 465,
"column": 2
} | {
"line": 465,
"column": 70
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Complex | {
"line": 78,
"column": 4
} | {
"line": 78,
"column": 83
} | [
{
"pp": "E : 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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 556,
"column": 2
} | {
"line": 556,
"column": 49
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 563,
"column": 2
} | {
"line": 563,
"column": 49
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 570,
"column": 2
} | {
"line": 570,
"column": 49
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Complex | {
"line": 134,
"column": 4
} | {
"line": 134,
"column": 29
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 577,
"column": 2
} | {
"line": 577,
"column": 49
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 605,
"column": 2
} | {
"line": 605,
"column": 55
} | [
{
"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... | 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.MFDeriv.Tangent | {
"line": 91,
"column": 6
} | {
"line": 91,
"column": 17
} | [
{
"pp": "case e_f.e_f.hc.h\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 : IsMani... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable | {
"line": 68,
"column": 2
} | {
"line": 68,
"column": 46
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable | {
"line": 83,
"column": 2
} | {
"line": 83,
"column": 46
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable | {
"line": 238,
"column": 2
} | {
"line": 238,
"column": 46
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable | {
"line": 288,
"column": 2
} | {
"line": 288,
"column": 46
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable | {
"line": 466,
"column": 13
} | {
"line": 466,
"column": 24
} | [
{
"pp": "case empty\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 : FiberB... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable | {
"line": 468,
"column": 4
} | {
"line": 468,
"column": 38
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable | {
"line": 564,
"column": 4
} | {
"line": 564,
"column": 15
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable | {
"line": 644,
"column": 6
} | {
"line": 644,
"column": 29
} | [
{
"pp": "case h\n𝕜 : Type u_1\nF₁ : Type u_2\nF₂ : Type u_3\nB₁ : Type u_4\nB₂ : Type u_5\nM : Type u_6\nE₁ : B₁ → Type u_7\nE₂ : B₂ → Type u_8\ninst✝³¹ : NontriviallyNormedField 𝕜\ninst✝³⁰ : (x : B₁) → AddCommGroup (E₁ x)\ninst✝²⁹ : (x : B₁) → Module 𝕜 (E₁ x)\ninst✝²⁸ : NormedAddCommGroup F₁\ninst✝²⁷ : Norm... | inCoordinates_eq hm h'm | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 680,
"column": 2
} | {
"line": 680,
"column": 34
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁴ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\nM' : Type u_21\ninst✝¹ : TopologicalS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 694,
"column": 32
} | {
"line": 694,
"column": 74
} | [
{
"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_21\ninst✝¹ : TopologicalS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 706,
"column": 33
} | {
"line": 706,
"column": 75
} | [
{
"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_21\ninst✝¹ : TopologicalS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 719,
"column": 2
} | {
"line": 719,
"column": 53
} | [
{
"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_21\ninst✝¹ : TopologicalS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 732,
"column": 2
} | {
"line": 732,
"column": 53
} | [
{
"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_21\ninst✝¹ : TopologicalS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 740,
"column": 2
} | {
"line": 740,
"column": 34
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁴ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\nM' : Type u_21\ninst✝¹ : TopologicalS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 748,
"column": 2
} | {
"line": 748,
"column": 34
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁴ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\nM' : Type u_21\ninst✝¹ : TopologicalS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 806,
"column": 13
} | {
"line": 806,
"column": 24
} | [
{
"pp": "case empty\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\nE' : Type u_5\ninst✝¹ : N... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 935,
"column": 21
} | {
"line": 935,
"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\ns : Set M\nz : M\nF' : Type u_21\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 935,
"column": 18
} | {
"line": 935,
"column": 65
} | [
{
"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... | by simpa only [mfld_simps] using hp.2.mul' hq.2 | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 962,
"column": 12
} | {
"line": 962,
"column": 34
} | [
{
"pp": "case zero\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' : Typ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 963,
"column": 17
} | {
"line": 963,
"column": 39
} | [
{
"pp": "case succ\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' : Typ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 1003,
"column": 13
} | {
"line": 1003,
"column": 24
} | [
{
"pp": "case empty\n𝕜 : 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\nz : M\nF' : Ty... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 1076,
"column": 2
} | {
"line": 1076,
"column": 30
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁴ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\ns : Set M\nz : M\nF' : Type u_21\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 1081,
"column": 2
} | {
"line": 1081,
"column": 30
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁴ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\nz : M\nF' : Type u_21\ninst✝¹ : Norme... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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