EuclideanGeometry.Sphere.isDiameter_iff_left_mem_and_pointReflection_center_left
∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : NormedSpace ℝ V] [inst_2 : MetricSpace P]
[inst_3 : NormedAddTorsor V P] {s : EuclideanGeometry.Sphere P} {p₁ p₂ : P},
s.IsDiameter p₁ p₂ ↔ p₁ ∈ s ∧ (Equiv.pointReflection s.center) p₁ = p₂- Defined in
- Mathlib.Geometry.Euclidean.Sphere.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- MetricSpacestatement and proof · cited by 1,684
- Equiv.Permstatement · cited by 1,375
- NormedAddTorsorstatement and proof · cited by 1,325
- EuclideanGeometry.Spherestatement and proof · cited by 233
- EuclideanGeometry.Sphere.centerstatement and proof · cited by 181
- midpointproof · cited by 123
- Equiv.pointReflectionstatement and proof · cited by 35
- EuclideanGeometry.Sphere.IsDiameterstatement and proof · cited by 31
Cited by1
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