EuclideanGeometry.Sphere.isDiameter_iff_left_mem_and_midpoint_eq_center
∀ {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 ∧ midpoint ℝ p₁ p₂ = s.center- Defined in
- Mathlib.Geometry.Euclidean.Sphere.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- NormedAddTorsorstatement and proof · cited by 1,325
- EuclideanGeometry.Spherestatement and proof · cited by 233
- EuclideanGeometry.Sphere.centerstatement and proof · cited by 181
- midpointstatement and proof · cited by 123
- EuclideanGeometry.Sphere.IsDiameterstatement and proof · cited by 31
- EuclideanGeometry.Sphere.IsDiameter.midpoint_eq_centerproof · cited by 11
- EuclideanGeometry.Sphere.IsDiameter.left_memproof · cited by 8
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