module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Geometry.Euclidean.Sphere.Tangent | {
"line": 111,
"column": 4
} | {
"line": 111,
"column": 15
} | {
"line": 111,
"column": 16
} | [
{
"pp": "case refine_1\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 : Sphere P\np q : P\nas : AffineSubspace ℝ P\nh : s.IsTangentAt p as\nx✝ : q ∈ s ∧ q ∈ as\nhs : q ∈ s\nhas : q ∈ as\nhd : s.radius ^ 2 = s.rad... | [
"case refine_1\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 : Sphere P\np q : P\nas : AffineSubspace ℝ P\nh : s.IsTangentAt p as\nx✝ : q ∈ s ∧ q ∈ as\nhs : q ∈ s\nhas : q ∈ as\nhd : s.radius ^ 2 = s.radius ^ 2 + di... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.Tangent | {
"line": 133,
"column": 4
} | {
"line": 133,
"column": 79
} | {
"line": 133,
"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\ns : Sphere P\nas : AffineSubspace ℝ P\np q : P\nh : s.IsTangentAt p as\nhq : q ∈ as\nhqp : q ≠ p\nthis : s.radius ^ 2 < dist q s.center ^ 2\n⊢ s.radius < dist ... | [
"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 : Sphere P\nas : AffineSubspace ℝ P\np q : P\nh : s.IsTangentAt p as\nhq : q ∈ as\nhqp : q ≠ p\nthis : s.radius ^ 2 < dist q s.center ^ 2\n⊢ s.radius < dist q s.center"
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.OrthRadius | {
"line": 299,
"column": 4
} | {
"line": 299,
"column": 15
} | {
"line": 299,
"column": 16
} | [
{
"pp": "case inr.inl\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 : Sphere P\np : P\nh : dist s.center s.center = s.radius\nhs : Subsingleton P\n⊢ s.radius = 0",
"ppTerm": "?inr.inl",
"assigned": false... | [
"case inr.inl\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 : Sphere P\np : P\nh : dist s.center s.center = s.radius\nhs : Subsingleton P\n⊢ s.radius = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.OrthRadius | {
"line": 318,
"column": 49
} | {
"line": 318,
"column": 60
} | {
"line": 318,
"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\nhf2 : Fact (Module.finrank ℝ V = 2)\ns : Sphere P\np : P\nhp : dist p s.center ≤ s.radius\nhpc : p ≠ s.center\nv : V\nhv : v ∈ (ℝ ∙ (p -ᵥ s.center))ᗮ\nhv1 : ‖v... | [
"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\nhf2 : Fact (Module.finrank ℝ V = 2)\ns : Sphere P\np : P\nhp : dist p s.center ≤ s.radius\nhpc : p ≠ s.center\nv : V\nhv : v ∈ (ℝ ∙ (p -ᵥ s.center))ᗮ\nhv1 : ‖v‖ = 1\nhr : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.OrthRadius | {
"line": 321,
"column": 4
} | {
"line": 321,
"column": 15
} | {
"line": 321,
"column": 16
} | [
{
"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\nhf2 : Fact (Module.finrank ℝ V = 2)\ns : Sphere P\np : P\nhp : dist p s.center ≤ s.radius\nhpc : p ≠ s.center\nv : V\nhv : v ∈ (ℝ ∙ (p -ᵥ s.center))ᗮ\nhv1 : ‖v... | [
"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\nhf2 : Fact (Module.finrank ℝ V = 2)\ns : Sphere P\np : P\nhp : dist p s.center ≤ s.radius\nhpc : p ≠ s.center\nv : V\nhv : v ∈ (ℝ ∙ (p -ᵥ s.center))ᗮ\nhv1 : ‖v‖ = 1\nhr : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.OrthRadius | {
"line": 337,
"column": 4
} | {
"line": 337,
"column": 32
} | {
"line": 337,
"column": 33
} | [
{
"pp": "case refine_1\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\nhf2 : Fact (Module.finrank ℝ V = 2)\ns : Sphere P\np : P\nhp : dist p s.center ≤ s.radius\nhpc : p ≠ s.center\nv : V\nhv : v ∈ (ℝ ∙ (p -ᵥ s.cent... | [
"case refine_1\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\nhf2 : Fact (Module.finrank ℝ V = 2)\ns : Sphere P\np : P\nhp : dist p s.center ≤ s.radius\nhpc : p ≠ s.center\nv : V\nhv : v ∈ (ℝ ∙ (p -ᵥ s.center))ᗮ\nhv1 :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.Tangent | {
"line": 413,
"column": 39
} | {
"line": 416,
"column": 21
} | {
"line": 418,
"column": 0
} | [
{
"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\ninst✝ : Nontrivial V\ns : Sphere P\n⊢ s.IsIntTangent s ↔ 0 ≤ s.radius",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [] | by
simp_rw [IsIntTangent, isIntTangentAt_self_iff_mem]
rw [← nonempty_iff]
simp [Set.Nonempty] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Geometry.Euclidean.Angle.Bisector | {
"line": 306,
"column": 8
} | {
"line": 306,
"column": 19
} | {
"line": 306,
"column": 20
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ninst✝¹ : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np p₁ p₂ p₃ : P\nha : AffineIndependent ℝ ![p₁, p₂, p₃]\nh : dist p ↑((orthogonalProjection line... | [
"V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ninst✝¹ : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np p₁ p₂ p₃ : P\nha : AffineIndependent ℝ ![p₁, p₂, p₃]\nh : dist p ↑((orthogonalProjection line[ℝ, p₁, p₂])... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Bisector | {
"line": 309,
"column": 8
} | {
"line": 309,
"column": 19
} | {
"line": 309,
"column": 20
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ninst✝¹ : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np p₁ p₂ p₃ : P\nha : AffineIndependent ℝ ![p₁, p₂, p₃]\nh : dist p ↑((orthogonalProjection line... | [
"V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ninst✝¹ : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np p₁ p₂ p₃ : P\nha : AffineIndependent ℝ ![p₁, p₂, p₃]\nh : dist p ↑((orthogonalProjection line[ℝ, p₁, p₂])... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.OrthRadius | {
"line": 368,
"column": 34
} | {
"line": 368,
"column": 45
} | {
"line": 368,
"column": 46
} | [
{
"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\nhf2 : Fact (Module.finrank ℝ V = 2)\ns : Sphere P\np : P\nhp : dist p s.center < s.radius\nhpc : p ≠ s.center\nv : ↥(s.orthRadius p).direction\nhv0 : v ≠ 0\nhv... | [
"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\nhf2 : Fact (Module.finrank ℝ V = 2)\ns : Sphere P\np : P\nhp : dist p s.center < s.radius\nhpc : p ≠ s.center\nv : ↥(s.orthRadius p).direction\nhv0 : v ≠ 0\nhv : ∀ (w : ↥(... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.OrthRadius | {
"line": 369,
"column": 58
} | {
"line": 369,
"column": 69
} | {
"line": 369,
"column": 70
} | [
{
"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\nhf2 : Fact (Module.finrank ℝ V = 2)\ns : Sphere P\np : P\nhp : dist p s.center < s.radius\nhpc : p ≠ s.center\nv : ↥(s.orthRadius p).direction\nhv : ∀ (w : ↥(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\nhf2 : Fact (Module.finrank ℝ V = 2)\ns : Sphere P\np : P\nhp : dist p s.center < s.radius\nhpc : p ≠ s.center\nv : ↥(s.orthRadius p).direction\nhv : ∀ (w : ↥(s.orthRadius ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.OrthRadius | {
"line": 377,
"column": 4
} | {
"line": 377,
"column": 15
} | {
"line": 377,
"column": 16
} | [
{
"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\nhf2 : Fact (Module.finrank ℝ V = 2)\ns : Sphere P\np : P\nhp : dist p s.center < s.radius\nhpc : p ≠ s.center\nv : ↥(s.orthRadius p).direction\nhv : ∀ (w : ↥(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\nhf2 : Fact (Module.finrank ℝ V = 2)\ns : Sphere P\np : P\nhp : dist p s.center < s.radius\nhpc : p ≠ s.center\nv : ↥(s.orthRadius p).direction\nhv : ∀ (w : ↥(s.orthRadius ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Sphere | {
"line": 256,
"column": 2
} | {
"line": 256,
"column": 13
} | {
"line": 256,
"column": 14
} | [
{
"pp": "case h\nV : Type u_3\nP : Type u_4\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\ns : Sphere P\np₁ p₂ : P\nhp₁ : p₁ ∈ s\nhp₂ : p₂ ∈ s\nh : p₁ ≠ p₂\nr : ℝ\nhr : r • («o».rot... | [
"case h\nV : Type u_3\nP : Type u_4\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\ns : Sphere P\np₁ p₂ : P\nhp₁ : p₁ ∈ s\nhp₂ : p₂ ∈ s\nh : p₁ ≠ p₂\nr : ℝ\nhr : r • («o».rotation ↑(π / ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Incenter | {
"line": 132,
"column": 4
} | {
"line": 132,
"column": 66
} | {
"line": 132,
"column": 66
} | [
{
"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\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\nt : Triangle ℝ P\ni₁ i₂ i₃ : Fin 3\nh₁₂ : i₁ ≠ i₂\nh₁₃ : i₁ ≠ i₃\nh₂₃ : i₂ ≠ i₃\n⊢ ∡ (touchpoint t... | [
"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\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\nt : Triangle ℝ P\ni₁ i₂ i₃ : Fin 3\nh₁₂ : i₁ ≠ i₂\nh₁₃ : i₁ ≠ i₃\nh₂₃ : i₂ ≠ i₃\n⊢ ∡ (touchpoint t {i₁} i₃) (t... | (t.touchpoint_singleton_sbtw h₁₂ h₁₃ h₂₃).symm.oangle_eq_right | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Sphere | {
"line": 294,
"column": 4
} | {
"line": 294,
"column": 15
} | {
"line": 294,
"column": 16
} | [
{
"pp": "case h\nV : Type u_3\nP : Type u_4\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\ns : Sphere P\np₁ p₂ : P\nhp₁ : p₁ ∈ s\nhp₂ : p₂ ∈ s\nh : p₁ ≠ p₂\n⊢ midpoint ℝ p₁ p₂ -ᵥ p₁... | [
"case h\nV : Type u_3\nP : Type u_4\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\ns : Sphere P\np₁ p₂ : P\nhp₁ : p₁ ∈ s\nhp₂ : p₂ ∈ s\nh : p₁ ≠ p₂\n⊢ ¬p₂ = p₁"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Incenter | {
"line": 227,
"column": 4
} | {
"line": 228,
"column": 11
} | {
"line": 228,
"column": 12
} | [
{
"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\nthis :\n ∀ (i : Fin (n + 1)),\n i ≠ 0 → ∑ j, ⟪s.points i -ᵥ s.points 0, (s.height j)⁻¹ ^ 2 • (s.points j -ᵥ s.... | [
"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\nthis :\n ∀ (i : Fin (n + 1)),\n i ≠ 0 → ∑ j, ⟪s.points i -ᵥ s.points 0, (s.height j)⁻¹ ^ 2 • (s.points j -ᵥ s.altitudeFoot... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Circumcenter | {
"line": 154,
"column": 37
} | {
"line": 154,
"column": 48
} | {
"line": 154,
"column": 49
} | [
{
"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\nι : Type u_3\nhne : Nonempty ι\ninst✝ : Finite ι\np : ι → P\nha : AffineIndependent ℝ p\nval✝ : Fintype ι\nhm :\n ∀ {ι : Type u_3} [hne : Nonempty ι] [Finite... | [
"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\nι : Type u_3\nhne : Nonempty ι\ninst✝ : Finite ι\np : ι → P\nha : AffineIndependent ℝ p\nval✝ : Fintype ι\nhm :\n ∀ {ι : Type u_3} [hne : Nonempty ι] [Finite ι] {p : ι →... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Sphere | {
"line": 500,
"column": 14
} | {
"line": 501,
"column": 81
} | {
"line": 501,
"column": 81
} | [
{
"pp": "case pos\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\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np₁ p₂ p₃ p₄ : P\nh : 2 • ∡ p₁ p₂ p₄ = 2 • ∡ p₁ p₃ p₄\nhc : Collinear ℝ {p₁, p₂, p₄}\nhe ... | [
"case pos\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\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np₁ p₂ p₃ p₄ : P\nh : 2 • ∡ p₁ p₂ p₄ = 2 • ∡ p₁ p₃ p₄\nhc : Collinear ℝ {p₁, p₂, p₄}\nhe : p₁ = p₄\n⊢... | Set.insert_eq_self.2
(Set.mem_insert_of_mem _ (Set.mem_insert_of_mem _ (Set.mem_singleton _))) | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Incenter | {
"line": 628,
"column": 2
} | {
"line": 628,
"column": 13
} | {
"line": 628,
"column": 14
} | [
{
"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\nsigns : Finset (Fin (n + 1))\nh : s.ExcenterExists signs\ni : Fin (n + 1)\nhf : s.excenter signs ∉ affineSpan ℝ (S... | [
"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\nsigns : Finset (Fin (n + 1))\nh : s.ExcenterExists signs\ni : Fin (n + 1)\nhf : s.excenter signs ∉ affineSpan ℝ (Set.range (s.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality | {
"line": 116,
"column": 4
} | {
"line": 116,
"column": 30
} | {
"line": 117,
"column": 2
} | [
{
"pp": "case inl\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y z : V\nhx : ‖x‖ = 1\nhy : ‖y‖ = 1\nhz : ‖z‖ = 1\nH : π < angle x y + angle y z\n⊢ angle x z ≤ angle x y + angle y z",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Real.instIsOrderedRin... | [] | linarith [angle_le_pi x z] | Mathlib.Tactic._aux_Mathlib_Tactic_Linarith_Frontend___elabRules_Mathlib_Tactic_linarith_1 | Mathlib.Tactic.linarith |
Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality | {
"line": 116,
"column": 4
} | {
"line": 116,
"column": 30
} | {
"line": 117,
"column": 2
} | [
{
"pp": "case inl\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y z : V\nhx : ‖x‖ = 1\nhy : ‖y‖ = 1\nhz : ‖z‖ = 1\nH : π < angle x y + angle y z\n⊢ angle x z ≤ angle x y + angle y z",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Real.instIsOrderedRin... | [] | linarith [angle_le_pi x z] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality | {
"line": 116,
"column": 4
} | {
"line": 116,
"column": 30
} | {
"line": 117,
"column": 2
} | [
{
"pp": "case inl\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y z : V\nhx : ‖x‖ = 1\nhy : ‖y‖ = 1\nhz : ‖z‖ = 1\nH : π < angle x y + angle y z\n⊢ angle x z ≤ angle x y + angle y z",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Real.instIsOrderedRin... | [] | linarith [angle_le_pi x z] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Euclidean.Triangle | {
"line": 184,
"column": 2
} | {
"line": 184,
"column": 13
} | {
"line": 184,
"column": 14
} | [
{
"pp": "case inr\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nhy : y ≠ 0\nhx : x ≠ 0\nh✝ : ↑(angle x y) = ↑(angle x (x + y) + angle y (x + y))\nh : angle x y + 0 • (2 * π) = angle x (x + y) + angle y (x + y)\nthis✝ : -1 < 0\nthis : 0 < 1\n⊢ angle x y = angle x (x + y) +... | [
"case inr\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nhy : y ≠ 0\nhx : x ≠ 0\nh✝ : ↑(angle x y) = ↑(angle x (x + y) + angle y (x + y))\nh : angle x y + 0 • (2 * π) = angle x (x + y) + angle y (x + y)\nthis✝ : -1 < 0\nthis : 0 < 1\n⊢ angle x y = angle x (x + y) + angle y (x ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Triangle | {
"line": 263,
"column": 4
} | {
"line": 263,
"column": 19
} | {
"line": 263,
"column": 19
} | [
{
"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\np₁ p₂ p₃ : P\n⊢ Real.sin (InnerProductGeometry.angle (p₃ -ᵥ p₁) (p₁ -ᵥ p₂)) =\n Real.sin (π - InnerProductGeometry.angle (p₃ -ᵥ p₁) (p₁ -ᵥ p₂))",
"ppTer... | [
"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\np₁ p₂ p₃ : P\n⊢ Real.sin (InnerProductGeometry.angle (p₃ -ᵥ p₁) (p₁ -ᵥ p₂)) =\n Real.sin (InnerProductGeometry.angle (p₃ -ᵥ p₁) (p₁ -ᵥ p₂))"
] | Real.sin_pi_sub | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Circumcenter | {
"line": 581,
"column": 4
} | {
"line": 581,
"column": 60
} | {
"line": 581,
"column": 61
} | [
{
"pp": "n : ℕ\ni₁ i₂ : Fin (n + 1)\nh : i₁ ≠ i₂\n⊢ Disjoint (if i₁ ∈ univ then {i₁} else ∅) (if i₂ ∈ univ then {i₂} else ∅)",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instDecidableTrue",
"Finset.univ",
"if_true",
"_private.Mathlib.Geometry.Euc... | [
"n : ℕ\ni₁ i₂ : Fin (n + 1)\nh : i₁ ≠ i₂\n⊢ i₁ ≠ i₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Incenter | {
"line": 707,
"column": 4
} | {
"line": 707,
"column": 15
} | {
"line": 707,
"column": 16
} | [
{
"pp": "case inl\nV : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\nn : ℕ\ninst✝¹ : NeZero n\ns : Simplex ℝ P n\ninst✝ : n.AtLeastTwo\ni j : Fin (n + 1)\nhij : {i} = {j}\n⊢ i = j",
"ppTerm": "?inl",
"assigned... | [
"case inl\nV : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\nn : ℕ\ninst✝¹ : NeZero n\ns : Simplex ℝ P n\ninst✝ : n.AtLeastTwo\ni j : Fin (n + 1)\nhij : {i} = {j}\n⊢ i = j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality | {
"line": 197,
"column": 4
} | {
"line": 197,
"column": 20
} | {
"line": 197,
"column": 21
} | [
{
"pp": "case pos\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y z : V\nhx : x = 0\n⊢ angle x z ≤ angle x y + angle y z",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real.partialOrder",
"Real.instLE",
"Real",
"ins... | [
"case pos\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y z : V\nhx : x = 0\n⊢ 0 ≤ angle y z"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality | {
"line": 199,
"column": 4
} | {
"line": 199,
"column": 20
} | {
"line": 199,
"column": 21
} | [
{
"pp": "case pos\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y z : V\nhx : ¬x = 0\nhy : y = 0\n⊢ angle x z ≤ angle x y + angle y z",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real.partialOrder",
"Real.instLE",
"Real... | [
"case pos\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y z : V\nhx : ¬x = 0\nhy : y = 0\n⊢ angle x z ≤ π"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality | {
"line": 201,
"column": 4
} | {
"line": 201,
"column": 20
} | {
"line": 201,
"column": 21
} | [
{
"pp": "case pos\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y z : V\nhx : ¬x = 0\nhy : ¬y = 0\nhz : z = 0\n⊢ angle x z ≤ angle x y + angle y z",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real.partialOrder",
"Real.instLE"... | [
"case pos\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y z : V\nhx : ¬x = 0\nhy : ¬y = 0\nhz : z = 0\n⊢ 0 ≤ angle x y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality | {
"line": 202,
"column": 2
} | {
"line": 202,
"column": 13
} | {
"line": 202,
"column": 14
} | [
{
"pp": "case neg\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y z : V\nhx : ¬x = 0\nhy : ¬y = 0\nhz : ¬z = 0\n⊢ angle x z ≤ angle x y + angle y z",
"ppTerm": "?neg✝",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case neg\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y z : V\nhx : ¬x = 0\nhy : ¬y = 0\nhz : ¬z = 0\n⊢ angle x z ≤ angle x y + angle y z"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Triangle | {
"line": 348,
"column": 25
} | {
"line": 348,
"column": 41
} | {
"line": 348,
"column": 42
} | [
{
"pp": "case pos\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\na b c p : P\nhb : a ≠ b\nhc : a ≠ c\nhp : Wbtw ℝ b p c\npb : p = b\n⊢ ∠ b a p + ∠ p a c = ∠ b a c",
"ppTerm": "?pos✝",
"assigned": true,
... | [
"case pos\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\na b c p : P\nhb : a ≠ b\nhc : a ≠ c\nhp : Wbtw ℝ b p c\npb : p = b\n⊢ ∠ b a b = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Triangle | {
"line": 349,
"column": 25
} | {
"line": 349,
"column": 41
} | {
"line": 349,
"column": 42
} | [
{
"pp": "case pos\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\na b c p : P\nhb : a ≠ b\nhc : a ≠ c\nhp : Wbtw ℝ b p c\npb : ¬p = b\npc : p = c\n⊢ ∠ b a p + ∠ p a c = ∠ b a c",
"ppTerm": "?pos✝",
"assigned... | [
"case pos\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\na b c p : P\nhb : a ≠ b\nhc : a ≠ c\nhp : Wbtw ℝ b p c\npb : ¬p = b\npc : p = c\n⊢ ∠ c a c = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality | {
"line": 217,
"column": 6
} | {
"line": 217,
"column": 45
} | {
"line": 218,
"column": 8
} | [
{
"pp": "case pos\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx z : V\nkx kz : ℝ≥0\nhy : kx • x + kz • z ≠ 0\nhkx : 0 < kx\nhkz : 0 < kz\nhz : z ≠ 0\n⊢ angle x z = angle x (kx • x + kz • z) + angle z (kx • x + kz • z)",
"ppTerm": "?pos✝",
"assigned": true,
"usedConst... | [
"case pos\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx z : V\nkx kz : ℝ≥0\nhy : kx • x + kz • z ≠ 0\nhkx : 0 < kx\nhkz : 0 < kz\nhz : z ≠ 0\n⊢ angle x z = angle x (↑kx • x + ↑kz • z) + angle z (↑kx • x + ↑kz • z)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality | {
"line": 221,
"column": 6
} | {
"line": 221,
"column": 45
} | {
"line": 222,
"column": 8
} | [
{
"pp": "case neg\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx z : V\nkx kz : ℝ≥0\nhy : kx • x + kz • z ≠ 0\nhkx : 0 < kx\nhkz : 0 < kz\nhz : z = 0\nhx : x ≠ 0\n⊢ angle z x = angle z (kz • z + kx • x) + angle x (kz • z + kx • x)",
"ppTerm": "?neg✝",
"assigned": true,
... | [
"case neg\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx z : V\nkx kz : ℝ≥0\nhy : kx • x + kz • z ≠ 0\nhkx : 0 < kx\nhkz : 0 < kz\nhz : z = 0\nhx : x ≠ 0\n⊢ angle z x = angle z (↑kz • z + ↑kx • x) + angle x (↑kz • z + ↑kx • x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Circumcenter | {
"line": 668,
"column": 80
} | {
"line": 670,
"column": 31
} | {
"line": 672,
"column": 0
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ns : AffineSubspace ℝ P\nps : Set P\nh : ps ⊆ ↑s\ninst✝¹ : Nonempty ↥s\nn : ℕ\ninst✝ : FiniteDimensional ℝ ↥s.direction\nhd : finrank ℝ ↥s.direction = n\nhc : ... | [] | by
rcases exists_circumradius_eq_of_cospherical_subset h hd hc with ⟨r, hr⟩
rw [hr sx₁ hsx₁, hr sx₂ hsx₂] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.MetricSpace.Congruence | {
"line": 99,
"column": 2
} | {
"line": 100,
"column": 9
} | {
"line": 100,
"column": 10
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nP₁ : Type u_3\nP₂ : Type u_4\ninst✝² : PseudoEMetricSpace P₁\ninst✝¹ : PseudoEMetricSpace P₂\nE : Type u_7\ninst✝ : EquivLike E ι' ι\nf : E\nv₁ : ι → P₁\nv₂ : ι → P₂\nh : v₁ ∘ ⇑f ≅ v₂ ∘ ⇑f\ni₁ i₂ : ι\n⊢ edist (v₁ i₁) (v₁ i₂) = edist (v₂ i₁) (v₂ i₂)",
"ppTerm": "?m.25",
... | [
"ι : Type u_1\nι' : Type u_2\nP₁ : Type u_3\nP₂ : Type u_4\ninst✝² : PseudoEMetricSpace P₁\ninst✝¹ : PseudoEMetricSpace P₂\nE : Type u_7\ninst✝ : EquivLike E ι' ι\nf : E\nv₁ : ι → P₁\nv₂ : ι → P₂\nh : v₁ ∘ ⇑f ≅ v₂ ∘ ⇑f\ni₁ i₂ : ι\n⊢ edist (v₁ i₁) (v₁ i₂) = edist (v₂ i₁) (v₂ i₂)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Congruence | {
"line": 85,
"column": 44
} | {
"line": 85,
"column": 73
} | {
"line": 85,
"column": 74
} | [
{
"pp": "V₁ : Type u_2\nV₂ : Type u_3\nP₁ : Type u_4\nP₂ : Type u_5\ninst✝⁷ : NormedAddCommGroup V₁\ninst✝⁶ : NormedAddCommGroup V₂\ninst✝⁵ : InnerProductSpace ℝ V₁\ninst✝⁴ : InnerProductSpace ℝ V₂\ninst✝³ : MetricSpace P₁\ninst✝² : MetricSpace P₂\ninst✝¹ : NormedAddTorsor V₁ P₁\ninst✝ : NormedAddTorsor V₂ P₂\n... | [
"V₁ : Type u_2\nV₂ : Type u_3\nP₁ : Type u_4\nP₂ : Type u_5\ninst✝⁷ : NormedAddCommGroup V₁\ninst✝⁶ : NormedAddCommGroup V₂\ninst✝⁵ : InnerProductSpace ℝ V₁\ninst✝⁴ : InnerProductSpace ℝ V₂\ninst✝³ : MetricSpace P₁\ninst✝² : MetricSpace P₂\ninst✝¹ : NormedAddTorsor V₁ P₁\ninst✝ : NormedAddTorsor V₂ P₂\na b c : P₁\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Congruence | {
"line": 86,
"column": 48
} | {
"line": 86,
"column": 77
} | {
"line": 86,
"column": 78
} | [
{
"pp": "V₁ : Type u_2\nV₂ : Type u_3\nP₁ : Type u_4\nP₂ : Type u_5\ninst✝⁷ : NormedAddCommGroup V₁\ninst✝⁶ : NormedAddCommGroup V₂\ninst✝⁵ : InnerProductSpace ℝ V₁\ninst✝⁴ : InnerProductSpace ℝ V₂\ninst✝³ : MetricSpace P₁\ninst✝² : MetricSpace P₂\ninst✝¹ : NormedAddTorsor V₁ P₁\ninst✝ : NormedAddTorsor V₂ P₂\n... | [
"V₁ : Type u_2\nV₂ : Type u_3\nP₁ : Type u_4\nP₂ : Type u_5\ninst✝⁷ : NormedAddCommGroup V₁\ninst✝⁶ : NormedAddCommGroup V₂\ninst✝⁵ : InnerProductSpace ℝ V₁\ninst✝⁴ : InnerProductSpace ℝ V₂\ninst✝³ : MetricSpace P₁\ninst✝² : MetricSpace P₂\ninst✝¹ : NormedAddTorsor V₁ P₁\ninst✝ : NormedAddTorsor V₂ P₂\na b c : P₁\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Triangle | {
"line": 487,
"column": 2
} | {
"line": 487,
"column": 13
} | {
"line": 487,
"column": 14
} | [
{
"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\na b c : P\nh : ¬Collinear ℝ {a, c, b}\n⊢ ∠ a c b ≤ ∠ a b c ↔ dist a b ≤ dist a c",
"ppTerm": "?m.68",
"assigned": false,
"usedConstants": [],
"... | [
"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\na b c : P\nh : ¬Collinear ℝ {a, c, b}\n⊢ ∠ a c b ≤ ∠ a b c ↔ dist a b ≤ dist a c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Congruence | {
"line": 116,
"column": 2
} | {
"line": 117,
"column": 63
} | {
"line": 119,
"column": 0
} | [
{
"pp": "ι : Type u_1\nV₁ : Type u_2\nV₂ : Type u_3\nP₁ : Type u_4\nP₂ : Type u_5\ninst✝⁷ : NormedAddCommGroup V₁\ninst✝⁶ : NormedAddCommGroup V₂\ninst✝⁵ : InnerProductSpace ℝ V₁\ninst✝⁴ : InnerProductSpace ℝ V₂\ninst✝³ : MetricSpace P₁\ninst✝² : MetricSpace P₂\ninst✝¹ : NormedAddTorsor V₁ P₁\ninst✝ : NormedAdd... | [] | simp_rw [real_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two,
vsub_sub_vsub_cancel_right, ← dist_eq_norm_vsub, h.dist_eq] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.Geometry.Euclidean.Inversion.Calculus | {
"line": 99,
"column": 37
} | {
"line": 99,
"column": 48
} | {
"line": 99,
"column": 49
} | [
{
"pp": "F : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\nc : F\nR : ℝ\nx : F\nhx : (fun x ↦ c + x) x ≠ c\nA : HasFDerivAt (fun x ↦ _root_.id x - c) (ContinuousLinearMap.id ℝ F) (c + x)\n⊢ ‖_root_.id (c + x) - c‖ ^ 2 ≠ 0",
"ppTerm": "?m.164",
"assigned": true,
"usedConstan... | [
"F : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\nc : F\nR : ℝ\nx : F\nhx : (fun x ↦ c + x) x ≠ c\nA : HasFDerivAt (fun x ↦ _root_.id x - c) (ContinuousLinearMap.id ℝ F) (c + x)\n⊢ ¬x = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Incenter | {
"line": 1181,
"column": 2
} | {
"line": 1181,
"column": 31
} | {
"line": 1181,
"column": 32
} | [
{
"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 j : Fin (n + 1)\nhne : i ≠ j\n⊢ 0 < s.touchpointWeights ∅ i j",
"ppTerm": "?m.45",
"assigned": false,
... | [
"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 j : Fin (n + 1)\nhne : i ≠ j\n⊢ 0 < s.touchpointWeights ∅ i j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Incenter | {
"line": 1201,
"column": 2
} | {
"line": 1201,
"column": 31
} | {
"line": 1201,
"column": 32
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\nn : ℕ\ninst✝¹ : NeZero n\ns : Simplex ℝ P n\ninst✝ : n.AtLeastTwo\ni j : Fin (n + 1)\nhne : i ≠ j\n⊢ 0 < s.touchpointWeights {i} i j",
"ppTerm": "?m.46",
... | [
"V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\nn : ℕ\ninst✝¹ : NeZero n\ns : Simplex ℝ P n\ninst✝ : n.AtLeastTwo\ni j : Fin (n + 1)\nhne : i ≠ j\n⊢ 0 < s.touchpointWeights {i} i j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Incenter | {
"line": 1219,
"column": 2
} | {
"line": 1219,
"column": 35
} | {
"line": 1219,
"column": 36
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\nn : ℕ\ninst✝¹ : NeZero n\ns : Simplex ℝ P n\ninst✝ : n.AtLeastTwo\ni j : Fin (n + 1)\nhne : i ≠ j\n⊢ s.touchpointWeights {i} j i < 0",
"ppTerm": "?m.46",
... | [
"V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\nn : ℕ\ninst✝¹ : NeZero n\ns : Simplex ℝ P n\ninst✝ : n.AtLeastTwo\ni j : Fin (n + 1)\nhne : i ≠ j\n⊢ s.touchpointWeights {i} j i < 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Incenter | {
"line": 1340,
"column": 6
} | {
"line": 1340,
"column": 40
} | {
"line": 1340,
"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\nt : Triangle ℝ P\ni₁ i₂ i₃ : Fin 3\nh₁₂ : i₁ ≠ i₂\nh₁₃ : i₁ ≠ i₃\nh₂₃ : i₂ ≠ i₃\n⊢ Sbtw ℝ (t.points i₁) (Simplex.touchpoint t ∅ i₂) (t.points i₃)",
"ppTerm... | [
"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\nt : Triangle ℝ P\ni₁ i₂ i₃ : Fin 3\nh₁₂ : i₁ ≠ i₂\nh₁₃ : i₁ ≠ i₃\nh₂₃ : i₂ ≠ i₃\n⊢ Simplex.touchpoint t ∅ i₂ ∈ (Simplex.face t ⋯).interior"
] | ← t.mem_interior_face_iff_sbtw h₁₃ | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Incenter | {
"line": 1348,
"column": 6
} | {
"line": 1348,
"column": 40
} | {
"line": 1348,
"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\nt : Triangle ℝ P\ni₁ i₂ i₃ : Fin 3\nh₁₂ : i₁ ≠ i₂\nh₁₃ : i₁ ≠ i₃\nh₂₃ : i₂ ≠ i₃\n⊢ Sbtw ℝ (t.points i₁) (Simplex.touchpoint t {i₂} i₂) (t.points i₃)",
"ppT... | [
"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\nt : Triangle ℝ P\ni₁ i₂ i₃ : Fin 3\nh₁₂ : i₁ ≠ i₂\nh₁₃ : i₁ ≠ i₃\nh₂₃ : i₂ ≠ i₃\n⊢ Simplex.touchpoint t {i₂} i₂ ∈ (Simplex.face t ⋯).interior"
] | ← t.mem_interior_face_iff_sbtw h₁₃ | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.NinePointCircle | {
"line": 72,
"column": 23
} | {
"line": 72,
"column": 34
} | {
"line": 72,
"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.48",
"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.Incenter | {
"line": 1365,
"column": 4
} | {
"line": 1365,
"column": 68
} | {
"line": 1366,
"column": 4
} | [
{
"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\nt : Triangle ℝ P\ni₁ i₂ i₃ : Fin 3\nh₁₂ : i₁ ≠ i₂\nh₁₃ : i₁ ≠ i₃\nh₂₃ : i₂ ≠ i₃\nhw : Simplex.touchpointWeights t {i₁} i₂ i₁ + Simplex.touchpointWeights t {i₁}... | [
"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\nt : Triangle ℝ P\ni₁ i₂ i₃ : Fin 3\nh₁₂ : i₁ ≠ i₂\nh₁₃ : i₁ ≠ i₃\nh₂₃ : i₂ ≠ i₃\nhw : Simplex.touchpointWeights t {i₁} i₂ i₁ + Simplex.touchpointWeights t {i₁} i₂ i₃ = 1\n... | have h : i = i₁ ∨ i = i₂ ∨ i = i₃ := by clear hw; decide +revert | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Geometry.Euclidean.NinePointCircle | {
"line": 102,
"column": 28
} | {
"line": 102,
"column": 39
} | {
"line": 102,
"column": 40
} | [
{
"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",
"ppTerm": "?m.75",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.NinePointCircle | {
"line": 105,
"column": 26
} | {
"line": 105,
"column": 37
} | {
"line": 105,
"column": 38
} | [
{
"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",
"ppTerm": "?m.135",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.Similarity | {
"line": 67,
"column": 34
} | {
"line": 67,
"column": 45
} | {
"line": 67,
"column": 46
} | [
{
"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)",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"... | [
"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) = edist (v₂ i₁) (v₂ i₂)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.NinePointCircle | {
"line": 112,
"column": 4
} | {
"line": 112,
"column": 15
} | {
"line": 112,
"column": 16
} | [
{
"pp": "case 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)",
"ppTerm": "?left",
"ass... | [
"case 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.points)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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": 157,
"column": 30
} | {
"line": 157,
"column": 41
} | {
"line": 157,
"column": 42
} | [
{
"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.211",
"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": 181,
"column": 55
} | {
"line": 181,
"column": 80
} | {
"line": 181,
"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": 187,
"column": 50
} | {
"line": 187,
"column": 61
} | {
"line": 187,
"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": 279,
"column": 27
} | {
"line": 279,
"column": 38
} | {
"line": 279,
"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.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.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.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.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.Euclidean.MongePoint | {
"line": 689,
"column": 70
} | {
"line": 689,
"column": 81
} | {
"line": 689,
"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": 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.Manifold.VectorBundle.Tangent | {
"line": 64,
"column": 55
} | {
"line": 64,
"column": 79
} | {
"line": 65,
"column": 2
} | [
{
"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.Geometry.Manifold.MFDeriv.Atlas | {
"line": 377,
"column": 4
} | {
"line": 377,
"column": 15
} | {
"line": 377,
"column": 16
} | [
{
"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... | [
"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\nhx : x ∈ (cha... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.Tangent | {
"line": 406,
"column": 6
} | {
"line": 406,
"column": 35
} | {
"line": 406,
"column": 36
} | [
{
"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... | [
"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\ninst✝⁸ : Topolo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.Tangent | {
"line": 413,
"column": 6
} | {
"line": 413,
"column": 35
} | {
"line": 413,
"column": 36
} | [
{
"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... | [
"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\ninst✝⁸ : Topolo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.Tangent | {
"line": 447,
"column": 2
} | {
"line": 447,
"column": 33
} | {
"line": 447,
"column": 34
} | [
{
"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,... | [
"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 ({ toFun := fun x ↦ (x.proj, x.snd), invFun := fu... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Diffeomorph | {
"line": 292,
"column": 4
} | {
"line": 292,
"column": 60
} | {
"line": 293,
"column": 6
} | [
{
"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... | [
"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\ninst✝⁸ : Topolo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Diffeomorph | {
"line": 318,
"column": 4
} | {
"line": 318,
"column": 60
} | {
"line": 319,
"column": 6
} | [
{
"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... | [
"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 : TopologicalSpac... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Diffeomorph | {
"line": 419,
"column": 4
} | {
"line": 419,
"column": 15
} | {
"line": 419,
"column": 16
} | [
{
"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... | [
"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 : TopologicalSp... | 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.Manifold.Complex | {
"line": 134,
"column": 4
} | {
"line": 134,
"column": 29
} | {
"line": 134,
"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.MFDeriv.Tangent | {
"line": 91,
"column": 6
} | {
"line": 91,
"column": 17
} | {
"line": 91,
"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": 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.IsManifold.InteriorBoundary | {
"line": 558,
"column": 2
} | {
"line": 558,
"column": 49
} | {
"line": 558,
"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": 565,
"column": 2
} | {
"line": 565,
"column": 49
} | {
"line": 565,
"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": 572,
"column": 2
} | {
"line": 572,
"column": 49
} | {
"line": 572,
"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": 579,
"column": 2
} | {
"line": 579,
"column": 49
} | {
"line": 579,
"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": 607,
"column": 2
} | {
"line": 607,
"column": 55
} | {
"line": 608,
"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": 234,
"column": 2
} | {
"line": 234,
"column": 46
} | {
"line": 235,
"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": 283,
"column": 2
} | {
"line": 283,
"column": 46
} | {
"line": 283,
"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.MFDeriv.SpecificFunctions | {
"line": 681,
"column": 2
} | {
"line": 681,
"column": 34
} | {
"line": 681,
"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\nM' : Type u_21\ninst✝¹ : TopologicalS... | [
"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 : TopologicalSpace M'\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 695,
"column": 32
} | {
"line": 695,
"column": 74
} | {
"line": 695,
"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... | [
"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 : TopologicalSpace M'\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 707,
"column": 33
} | {
"line": 707,
"column": 75
} | {
"line": 707,
"column": 76
} | [
{
"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... | [
"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 : TopologicalSpace M'\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable | {
"line": 465,
"column": 4
} | {
"line": 465,
"column": 38
} | {
"line": 465,
"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.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 741,
"column": 2
} | {
"line": 741,
"column": 34
} | {
"line": 741,
"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\nM' : Type u_21\ninst✝¹ : TopologicalS... | [
"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 : TopologicalSpace M'\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 749,
"column": 2
} | {
"line": 749,
"column": 34
} | {
"line": 749,
"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\nM' : Type u_21\ninst✝¹ : TopologicalS... | [
"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 : TopologicalSpace M'\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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