EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_wbtw
∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : MetricSpace P]
[inst_3 : NormedAddTorsor V P] {s : EuclideanGeometry.Sphere P} {p₁ p₂ : P},
s.IsDiameter p₁ p₂ ↔ p₁ ∈ s ∧ p₂ ∈ s ∧ Wbtw ℝ p₁ s.center p₂- Defined in
- Mathlib.Geometry.Euclidean.Sphere.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- InnerProductSpacestatement and proof · cited by 3,523
- MetricSpacestatement and proof · cited by 1,684
- Dist.distproof · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
- EuclideanGeometry.Spherestatement and proof · cited by 233
- two_mulproof · cited by 232
- EuclideanGeometry.Sphere.centerstatement and proof · cited by 181
- Wbtwstatement and proof · cited by 165
- EuclideanGeometry.Sphere.radiusproof · cited by 123
- EuclideanGeometry.Sphere.IsDiameterstatement and proof · cited by 31
Cited by2
Results whose statement or proof uses this declaration.
- EuclideanGeometry.Sphere.center_mem_affineSpan_pair_iff_isDiameterproof · cited by 0
- EuclideanGeometry.Sphere.angle_center_eq_pi_iff_isDiameterproof · cited by 0