module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 602,
"column": 8
} | {
"line": 602,
"column": 19
} | [
{
"pp": "case inl.inr\nV : Type u_1\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nw y z : V\nh : InnerProductGeometry.angle w 0 = InnerProductGeometry.angle y z\nhs : (o.oangle w 0).sign = (o.oangle y z).sign\n⊢ (o.oangle w 0).sign =... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 603,
"column": 8
} | {
"line": 603,
"column": 19
} | [
{
"pp": "case inr.inl\nV : Type u_1\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nw x z : V\nh : InnerProductGeometry.angle w x = InnerProductGeometry.angle 0 z\nhs : (o.oangle w x).sign = (o.oangle 0 z).sign\n⊢ (o.oangle w x).sign =... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 604,
"column": 8
} | {
"line": 604,
"column": 19
} | [
{
"pp": "case inr.inr\nV : Type u_1\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nw x y : V\nh : InnerProductGeometry.angle w x = InnerProductGeometry.angle y 0\nhs : (o.oangle w x).sign = (o.oangle y 0).sign\n⊢ (o.oangle w x).sign =... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 608,
"column": 8
} | {
"line": 608,
"column": 19
} | [
{
"pp": "case inl.inl\nV : Type u_1\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nx y z : V\nhsyz : (o.oangle y z).sign = 0\nh : InnerProductGeometry.angle 0 x = InnerProductGeometry.angle y z\nhs : (o.oangle 0 x).sign = (o.oangle y ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle | {
"line": 505,
"column": 2
} | {
"line": 505,
"column": 18
} | [
{
"pp": "case neg.h\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nhd2 : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nx : V\nh : x ≠ 0\nr : ℝ\nhr : ¬r = 0\nhx : -x = r⁻¹ • (o.rotation ↑(π / 2)) (r • (o.rotation ↑(π / 2)) x)\n⊢ r • (o.rotation ↑(π / 2)) x ≠ 0",
"usedCons... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 609,
"column": 8
} | {
"line": 609,
"column": 19
} | [
{
"pp": "case inl.inr\nV : Type u_1\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nw y z : V\nhsyz : (o.oangle y z).sign = 0\nh : InnerProductGeometry.angle w 0 = InnerProductGeometry.angle y z\nhs : (o.oangle w 0).sign = (o.oangle y ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 610,
"column": 8
} | {
"line": 610,
"column": 19
} | [
{
"pp": "case inr.inl\nV : Type u_1\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nw x z : V\nhswx : (o.oangle w x).sign = 0\nh : InnerProductGeometry.angle w x = InnerProductGeometry.angle 0 z\nhs : (o.oangle w x).sign = (o.oangle 0 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle | {
"line": 518,
"column": 2
} | {
"line": 518,
"column": 18
} | [
{
"pp": "case neg.h\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nhd2 : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nx : V\nh : x ≠ 0\nr : ℝ\nhr : ¬r = 0\nhx : x = r⁻¹ • (o.rotation ↑(π / 2)) (-(r • (o.rotation ↑(π / 2)) x))\n⊢ -(r • (o.rotation ↑(π / 2)) x) ≠ 0",
"use... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 611,
"column": 8
} | {
"line": 611,
"column": 19
} | [
{
"pp": "case inr.inr\nV : Type u_1\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nw x y : V\nhswx : (o.oangle w x).sign = 0\nh : InnerProductGeometry.angle w x = InnerProductGeometry.angle y 0\nhs : (o.oangle w x).sign = (o.oangle y ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 620,
"column": 6
} | {
"line": 620,
"column": 49
} | [
{
"pp": "V : Type u_1\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nw x y z : V\nh : InnerProductGeometry.angle w x = InnerProductGeometry.angle y z\nhs : (o.oangle w x).sign = (o.oangle y z).sign\nh0 : (w = 0 ∨ x = 0) ∨ y = 0 ∨ z = ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 623,
"column": 6
} | {
"line": 623,
"column": 49
} | [
{
"pp": "V : Type u_1\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nw x y z : V\nh : InnerProductGeometry.angle w x = InnerProductGeometry.angle y z\nhs : (o.oangle w x).sign = (o.oangle y z).sign\nh0 : (w = 0 ∨ x = 0) ∨ y = 0 ∨ z = ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 691,
"column": 4
} | {
"line": 691,
"column": 15
} | [
{
"pp": "case refine_2\nV : Type u_1\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nx y : V\nhx : x ≠ 0\nhy : y ≠ 0\nh : InnerProductGeometry.angle x y = 0\nha : o.oangle x y = ↑0 ∨ o.oangle x y = -↑0\n⊢ o.oangle x y = 0",
"usedCo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 707,
"column": 4
} | {
"line": 707,
"column": 15
} | [
{
"pp": "case neg.refine_2\nV : Type u_1\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nx y : V\nhx : ¬x = 0\nhy : ¬y = 0\nh : InnerProductGeometry.angle x y = π\nha : o.oangle x y = ↑π ∨ o.oangle x y = -↑π\n⊢ o.oangle x y = ↑π",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 755,
"column": 2
} | {
"line": 755,
"column": 55
} | [
{
"pp": "case neg\nV : Type u_1\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nx y : V\nhx : ¬x = 0\nhy : ¬y = 0\n⊢ (o.oangle x (-y)).sign = -(o.oangle x y).sign",
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
... | rw [o.oangle_neg_right hx hy, Real.Angle.sign_add_pi] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 757,
"column": 58
} | {
"line": 757,
"column": 69
} | [
{
"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)\np₁ p₂ p₃ p₄ : P\nh : Sbtw ℝ p₁ p₂ p₃\n⊢ Collinear ℝ {p₁, p₂, p₂, p₃}",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 766,
"column": 4
} | {
"line": 766,
"column": 36
} | [
{
"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)\np₁ p₂ p₃ p₄ : P\nh : Wbtw ℝ p₁ p₂ p₃\nhne : p₁ ≠ p₂\n⊢ Collinear ℝ {p₁, p₂, p₁, p₃}",
"usedCon... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle | {
"line": 733,
"column": 91
} | {
"line": 737,
"column": 52
} | [
{
"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)\np₁ p₂ p₃ : P\nh : ∡ p₁ p₂ p₃ = ↑(π / 2)\n⊢ dist p₃ p₂ / (∡ p₃ p₁ p₂).sin = dist p₁ p₃",
"usedC... | by
have hs : (∡ p₃ p₁ p₂).sign = 1 := by rw [← oangle_rotate_sign, h, Real.Angle.sign_coe_pi_div_two]
rw [oangle_eq_angle_of_sign_eq_one hs, angle_comm, Real.Angle.sin_coe, dist_comm p₁ p₃,
dist_div_sin_angle_of_angle_eq_pi_div_two (angle_rev_eq_pi_div_two_of_oangle_eq_pi_div_two h)
(Or.inl (right_ne_of_o... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 900,
"column": 4
} | {
"line": 900,
"column": 15
} | [
{
"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)\np₁ p₂ p₃ p₄ : P\nh₁₂ : p₁ ≠ p₂\nha : ∡ p₁ p₂ p₃ = ∡ p₃ p₂ p₄\nhs : (affineSpan ℝ {p₁, p₂}).SOppSid... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 820,
"column": 6
} | {
"line": 820,
"column": 22
} | [
{
"pp": "case refine_1\nV : Type u_1\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nx y : V\nr : ℝ\nh : ¬(o.oangle x y = 0 ∨ o.oangle x y = ↑π)\nh' : ∀ (r' : ℝ), o.oangle x (r' • x + y) ≠ 0 ∧ o.oangle x (r' • x + y) ≠ ↑π\ns : Set (V ×... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.SignedDist | {
"line": 54,
"column": 20
} | {
"line": 54,
"column": 50
} | [
{
"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\nv x y : V\n⊢ ContinuousAffineMap.const ℝ P ⟪-NormedSpace.normalize v, x + y⟫ =\n ContinuousAffineMap.const ℝ P ⟪-NormedSpace.normalize v, x⟫ +\n Contin... | by ext; simp [inner_add_right] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 821,
"column": 6
} | {
"line": 821,
"column": 22
} | [
{
"pp": "case refine_2\nV : Type u_1\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nx y : V\nr : ℝ\nh : ¬(o.oangle x y = 0 ∨ o.oangle x y = ↑π)\nh' : ∀ (r' : ℝ), o.oangle x (r' • x + y) ≠ 0 ∧ o.oangle x (r' • x + y) ≠ ↑π\ns : Set (V ×... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.SignedDist | {
"line": 97,
"column": 2
} | {
"line": 97,
"column": 13
} | [
{
"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\np q : P\n⊢ ((signedDist 0) p) q = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.SignedDist | {
"line": 100,
"column": 2
} | {
"line": 100,
"column": 13
} | [
{
"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\nv : V\np q : P\n⊢ ((signedDist (-v)) p) q = -((signedDist v) p) q",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.PerpBisector | {
"line": 106,
"column": 2
} | {
"line": 106,
"column": 51
} | [
{
"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 : P\n⊢ p₂ ∈ perpBisector p₁ p₂ ↔ p₁ = p₂",
"usedConstants": [
"NormedCommRing.toNormedRing",
"AddGroup.toSubtractionMonoid",
"Norm.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.SignedDist | {
"line": 105,
"column": 2
} | {
"line": 105,
"column": 17
} | [
{
"pp": "case h.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\nv w : V\nr : ℝ\nleft✝ : r > 0\nright✝ : r • v = w\np q : P\n⊢ ((signedDist v) p) q = ((signedDist w) p) q",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.PerpBisector | {
"line": 136,
"column": 40
} | {
"line": 136,
"column": 83
} | [
{
"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 : P\nh_sbtw : Sbtw ℝ a b c\nh_inner : ⟪p -ᵥ a, b -ᵥ a⟫ = 0\nt : ℝ\nhb_eq : (AffineMap.lineMap a c) t = b\nht0 : 0 < t\nht1 : t < 1\nhb : b -ᵥ a = t • (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.PerpBisector | {
"line": 142,
"column": 2
} | {
"line": 142,
"column": 45
} | [
{
"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 : P\nh_sbtw : Sbtw ℝ a b c\nh_inner : ⟪p -ᵥ a, b -ᵥ a⟫ = 0\nt : ℝ\nhb_eq : (AffineMap.lineMap a c) t = b\nht0 : 0 < t\nht1 : t < 1\nhb : b -ᵥ a = t • (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.SignedDist | {
"line": 149,
"column": 2
} | {
"line": 149,
"column": 62
} | [
{
"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\nv : V\np q : P\nh : ⟪v, p -ᵥ q⟫ = 0\nr : P\n⊢ ((signedDist v) p) r = ((signedDist v) q) r",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.SignedDist | {
"line": 153,
"column": 2
} | {
"line": 153,
"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\nv : V\np q r : P\nh : ⟪v, q -ᵥ r⟫ = 0\n⊢ ((signedDist v) p) q = ((signedDist v) p) r",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.PerpBisector | {
"line": 155,
"column": 2
} | {
"line": 155,
"column": 45
} | [
{
"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 : P\nh_inner : ⟪p -ᵥ a, c -ᵥ a⟫ = 0\nt : ℝ\nhb_eq : (AffineMap.lineMap a c) t = b\nht0 : 0 ≤ t\nht1 : t ≤ 1\nh_sq_ineq : dist p b ^ 2 ≤ dist p c ^ 2\n⊢... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.SignedDist | {
"line": 157,
"column": 2
} | {
"line": 157,
"column": 13
} | [
{
"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\nv : V\np q : P\nh : ⟪v, q -ᵥ p⟫ = 0\n⊢ ((signedDist v) p) q = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.SignedDist | {
"line": 217,
"column": 2
} | {
"line": 217,
"column": 13
} | [
{
"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\nv : V\np q : P\nc : ℝ\n⊢ ((signedDist v) ((AffineMap.lineMap p q) c)) p = -c * ((signedDist v) p) q",
"usedConstants": [
"ContinuousAffineMap.lineMap... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.SignedDist | {
"line": 221,
"column": 2
} | {
"line": 221,
"column": 13
} | [
{
"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\nv : V\np q : P\nc : ℝ\n⊢ ((signedDist v) p) ((AffineMap.lineMap p q) c) = c * ((signedDist v) p) q",
"usedConstants": [
"Eq.mpr",
"InnerProduct... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.SignedDist | {
"line": 225,
"column": 2
} | {
"line": 225,
"column": 13
} | [
{
"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\nv : V\np q : P\nc : ℝ\n⊢ ((signedDist v) ((AffineMap.lineMap p q) c)) q = (1 - c) * ((signedDist v) p) q",
"usedConstants": [
"ContinuousAffineMap.li... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.SignedDist | {
"line": 229,
"column": 2
} | {
"line": 229,
"column": 13
} | [
{
"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\nv : V\np q : P\nc : ℝ\n⊢ ((signedDist v) q) ((AffineMap.lineMap p q) c) = (c - 1) * ((signedDist v) p) q",
"usedConstants": [
"Eq.mpr",
"InnerP... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.SignedDist | {
"line": 284,
"column": 2
} | {
"line": 284,
"column": 13
} | [
{
"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\np q : P\n⊢ (affineSpan ℝ {q}).signedInfDist p = (signedDist (p -ᵥ q)) q",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Basic | {
"line": 107,
"column": 30
} | {
"line": 107,
"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\nv : V\np₁ p₂ : P\nhv : v ≠ 0\nr : ℝ\n⊢ ⟪v, v⟫ ≠ 0",
"usedConstants": [
"NormedCommRing.toNormedRing",
"AddGroup.toSubtractionMonoid",
"No... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.Basic | {
"line": 213,
"column": 2
} | {
"line": 213,
"column": 26
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : NormedSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\ninst✝ : Nontrivial V\ns : Sphere P\nh : 0 ≤ s.radius\nv : V\nhv : v ∈ Metric.sphere 0 s.radius\n⊢ v +ᵥ s.center ∈ Metric.sphere s.center s.radius",
"usedConstan... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 999,
"column": 14
} | {
"line": 999,
"column": 29
} | [
{
"pp": "case inl\nV : Type u_1\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nx y z : V\nhx : x ≠ 0\nhz : z ≠ 0\nhy : ¬y = 0\nhr : ¬SameRay ℝ x z\nhs : ¬(o.oangle x y).sign = (o.oangle y z).sign\nhn : o.oangle x y ≠ o.oangle y z\nhe ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 999,
"column": 14
} | {
"line": 999,
"column": 29
} | [
{
"pp": "case inr\nV : Type u_1\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nx y z : V\nhx : x ≠ 0\nhz : z ≠ 0\nhy : ¬y = 0\nhr : ¬SameRay ℝ x z\nhs : ¬(o.oangle x y).sign = (o.oangle y z).sign\nhn : o.oangle x y ≠ o.oangle y z\nhe ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.Basic | {
"line": 385,
"column": 30
} | {
"line": 385,
"column": 45
} | [
{
"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\nhs : Cospherical s\np : Fin 3 → P\nhps : Set.range p ⊆ s\nhpi : Function.Injective p\nv : V\nhv : ∀ (i : Fin 3), ∃ r, p i = r • v +ᵥ p 0\nh : v = 0\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.Basic | {
"line": 397,
"column": 4
} | {
"line": 397,
"column": 21
} | [
{
"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\np : Fin 3 → P\nhps : Set.range p ⊆ s\nhpi : Function.Injective p\nv : V\nhv0 : v ≠ 0\nc : P\nr : ℝ\nhs : ∀ p ∈ s, dist p c = r\nhs' : ∀ (i : Fin 3),... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.Basic | {
"line": 408,
"column": 4
} | {
"line": 408,
"column": 26
} | [
{
"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\np : Fin 3 → P\nhps : Set.range p ⊆ s\nhpi : Function.Injective p\nv : V\nhv0 : v ≠ 0\nc : P\nr : ℝ\nhs : ∀ p ∈ s, dist p c = r\nhs' : ∀ (i : Fin 3),... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.Basic | {
"line": 409,
"column": 34
} | {
"line": 409,
"column": 54
} | [
{
"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\np : Fin 3 → P\nhps : Set.range p ⊆ s\nhpi : Function.Injective p\nv : V\nhv0 : v ≠ 0\nc : P\nr : ℝ\nhs : ∀ p ∈ s, dist p c = r\nhs' : ∀ (i : Fin 3),... | hfn0' 1 (by decide), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Sphere.Basic | {
"line": 522,
"column": 8
} | {
"line": 522,
"column": 19
} | [
{
"pp": "case neg.refine_2.inl.refine_2\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\np₂ : P\nhp₂ : dist p₂ s.center ≤ s.radius\nhp₂' : dist p₂ s.center < dist s.center s.center\nhp₁ : dist s.center ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.Basic | {
"line": 530,
"column": 6
} | {
"line": 530,
"column": 17
} | [
{
"pp": "case neg.refine_2.inr\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\np₂ : P\nhp₂ : dist p₂ s.center ≤ s.radius\nhp₁ : dist s.center s.center = s.radius\nh : ¬s.center = p₂\nhp₂' : ‖p₂ -ᵥ s.ce... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.Tangent | {
"line": 87,
"column": 2
} | {
"line": 87,
"column": 13
} | [
{
"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\np q : P\nas : AffineSubspace ℝ P\nhp : s.IsTangentAt p as\nhq : s.IsTangentAt q as\nhqp : ⟪p -ᵥ q, p -ᵥ q⟫ = 0\nhpq : ⟪p -ᵥ q, q -ᵥ s.center⟫ = 0... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.Tangent | {
"line": 111,
"column": 4
} | {
"line": 111,
"column": 15
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.Tangent | {
"line": 133,
"column": 4
} | {
"line": 133,
"column": 79
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.OrthRadius | {
"line": 193,
"column": 4
} | {
"line": 193,
"column": 15
} | [
{
"pp": "case h.mp\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\nhp : dist p s.center = s.radius\np' : P\nhp's : p' ∈ s\nhp'i : p' ∈ s.orthRadius p\nh' : s.radius ^ 2 = s.radius ^ 2 + dist p' ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.OrthRadius | {
"line": 195,
"column": 4
} | {
"line": 195,
"column": 15
} | [
{
"pp": "case h.mpr\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\nhp : dist p' s.center = s.radius\n⊢ p' ∈ s ∧ p' ∈ s.orthRadius p'",
"usedConstants": [
"Eq.mpr",
"InnerProduc... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.OrthRadius | {
"line": 208,
"column": 6
} | {
"line": 208,
"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\ns : Sphere P\np q : P\nh : Metric.sphere s.center s.radius ∩ ↑(s.orthRadius p) = {q}\nhq : q ∈ Metric.sphere s.center s.radius ∩ ↑(s.orthRadius p)\nhr : 0 ≤ s.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.Tangent | {
"line": 413,
"column": 39
} | {
"line": 416,
"column": 21
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
... | by
simp_rw [IsIntTangent, isIntTangentAt_self_iff_mem]
rw [← nonempty_iff]
simp [Set.Nonempty] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Geometry.Euclidean.Sphere.OrthRadius | {
"line": 262,
"column": 8
} | {
"line": 262,
"column": 24
} | [
{
"pp": "case inl.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 p s.center < s.radius\nhp : p ≠ s.center\nhb : ℝ ∙ (p -ᵥ s.center) = ⊤\nhb' : ∀ (v : V), ∃ r, r • (p -ᵥ s.cente... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.OrthRadius | {
"line": 299,
"column": 4
} | {
"line": 299,
"column": 15
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.OrthRadius | {
"line": 318,
"column": 49
} | {
"line": 318,
"column": 60
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.OrthRadius | {
"line": 321,
"column": 4
} | {
"line": 321,
"column": 15
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.OrthRadius | {
"line": 337,
"column": 4
} | {
"line": 337,
"column": 32
} | [
{
"pp": "case h.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.ce... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Incenter | {
"line": 132,
"column": 4
} | {
"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... | (t.touchpoint_singleton_sbtw h₁₂ h₁₃ h₂₃).symm.oangle_eq_right | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Bisector | {
"line": 306,
"column": 8
} | {
"line": 306,
"column": 19
} | [
{
"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 :\n dist p ↑((orthogonalProjection (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Bisector | {
"line": 309,
"column": 8
} | {
"line": 309,
"column": 19
} | [
{
"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 :\n dist p ↑((orthogonalProjection (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.OrthRadius | {
"line": 368,
"column": 34
} | {
"line": 368,
"column": 45
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.OrthRadius | {
"line": 369,
"column": 58
} | {
"line": 369,
"column": 69
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Sphere.OrthRadius | {
"line": 377,
"column": 4
} | {
"line": 377,
"column": 15
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Sphere | {
"line": 256,
"column": 2
} | {
"line": 256,
"column": 13
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Sphere | {
"line": 294,
"column": 4
} | {
"line": 294,
"column": 15
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Sphere | {
"line": 500,
"column": 14
} | {
"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 ... | 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.Circumcenter | {
"line": 155,
"column": 37
} | {
"line": 155,
"column": 48
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Incenter | {
"line": 227,
"column": 4
} | {
"line": 228,
"column": 11
} | [
{
"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.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Circumcenter | {
"line": 582,
"column": 4
} | {
"line": 582,
"column": 60
} | [
{
"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 ∅)",
"usedConstants": [
"Eq.mpr",
"instDecidableTrue",
"Finset.univ",
"if_true",
"_private.Mathlib.Geometry.Euclidean.Circumcenter.0.Affine.Simplex.sum_refl... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Triangle | {
"line": 184,
"column": 2
} | {
"line": 184,
"column": 13
} | [
{
"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) +... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Triangle | {
"line": 263,
"column": 4
} | {
"line": 263,
"column": 19
} | [
{
"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\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))",
... | Real.sin_pi_sub | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Circumcenter | {
"line": 669,
"column": 80
} | {
"line": 671,
"column": 31
} | [
{
"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.Geometry.Euclidean.Triangle | {
"line": 340,
"column": 2
} | {
"line": 340,
"column": 41
} | [
{
"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 : Module.Oriented ℝ V (Fin 2)\ninst✝ : Fact (Module.finrank ℝ V = 2)\np₁ p₂ p₃ : P\nh21 : p₂ ≠ p₁\nh32 : p₃ ≠ p₂\nh13 : p₁ ≠ p₃\n⊢ ∡ p₁ p₂ p₃ + ∡ p₂ p₃... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Triangle | {
"line": 348,
"column": 25
} | {
"line": 348,
"column": 41
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"Rea... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Triangle | {
"line": 349,
"column": 25
} | {
"line": 349,
"column": 41
} | [
{
"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",
"usedConstants": [
"Eq.mpr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Incenter | {
"line": 628,
"column": 2
} | {
"line": 628,
"column": 13
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality | {
"line": 116,
"column": 4
} | {
"line": 116,
"column": 30
} | [
{
"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",
"usedConstants": [
"Real.instIsOrderedRing",
"Mathlib.Tactic.Ring.Common.neg_ze... | 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
} | [
{
"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",
"usedConstants": [
"Real.instIsOrderedRing",
"Mathlib.Tactic.Ring.Common.neg_ze... | 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
} | [
{
"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",
"usedConstants": [
"Real.instIsOrderedRing",
"Mathlib.Tactic.Ring.Common.neg_ze... | linarith [angle_le_pi x z] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Euclidean.Incenter | {
"line": 707,
"column": 4
} | {
"line": 707,
"column": 15
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Circumcenter | {
"line": 816,
"column": 6
} | {
"line": 816,
"column": 68
} | [
{
"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\np p₁ p₂ : P\nr : ℝ\nh₁ : ∀ (i : Fin (n + 1)), dist (s.points i) p₁ = r\nh₂ : ∀ (i : Fin (n + 1)), dist (s.points i) p₂ = r\nspan_s : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Triangle | {
"line": 462,
"column": 2
} | {
"line": 462,
"column": 13
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality | {
"line": 197,
"column": 4
} | {
"line": 197,
"column": 20
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"Real.partialOrder",
"Real.instLE",
"Real",
"instHDiv",
"Real.pi",
"Real.instAddM... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality | {
"line": 199,
"column": 4
} | {
"line": 199,
"column": 20
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"Real.partialOrder",
"Real.instLE",
"Real",
"instHDiv",
"Real.pi",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality | {
"line": 201,
"column": 4
} | {
"line": 201,
"column": 20
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"Real.partialOrder",
"Real.instLE",
"Real",
"Preorder.toLT",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality | {
"line": 202,
"column": 2
} | {
"line": 202,
"column": 13
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality | {
"line": 217,
"column": 6
} | {
"line": 217,
"column": 45
} | [
{
"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)",
"usedConstants": [
"InnerProductSpace.toNormedSpa... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality | {
"line": 221,
"column": 6
} | {
"line": 221,
"column": 45
} | [
{
"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)",
"usedConstants": [
"InnerProductSpace... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.Congruence | {
"line": 99,
"column": 2
} | {
"line": 100,
"column": 9
} | [
{
"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)",
"usedConstants": []... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Inversion.Calculus | {
"line": 99,
"column": 37
} | {
"line": 99,
"column": 48
} | [
{
"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",
"usedConstants": [
"NormedCommRing.toNormedRing",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Congruence | {
"line": 85,
"column": 44
} | {
"line": 85,
"column": 73
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Congruence | {
"line": 86,
"column": 48
} | {
"line": 86,
"column": 77
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Congruence | {
"line": 116,
"column": 2
} | {
"line": 117,
"column": 63
} | [
{
"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.Incenter | {
"line": 1181,
"column": 2
} | {
"line": 1181,
"column": 31
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Incenter | {
"line": 1201,
"column": 2
} | {
"line": 1201,
"column": 31
} | [
{
"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",
"usedConstants": []... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Incenter | {
"line": 1219,
"column": 2
} | {
"line": 1219,
"column": 35
} | [
{
"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",
"usedConstants": []... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Incenter | {
"line": 1340,
"column": 6
} | {
"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)",
"usedCo... | ← t.mem_interior_face_iff_sbtw h₁₃ | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Incenter | {
"line": 1348,
"column": 6
} | {
"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)",
"use... | ← t.mem_interior_face_iff_sbtw h₁₃ | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Incenter | {
"line": 1365,
"column": 4
} | {
"line": 1365,
"column": 68
} | [
{
"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\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.touchpointWeight... | 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__ |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.