EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_dist
∀ {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 ∧ dist p₁ p₂ = 2 * s.radius- Defined in
- Mathlib.Geometry.Euclidean.Sphere.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- Norm.normproof · cited by 5,413
- InnerProductSpacestatement and proof · cited by 3,523
- MetricSpacestatement and proof · cited by 1,684
- Dist.diststatement and proof · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
- VSub.vsubproof · cited by 817
- EuclideanGeometry.Spherestatement and proof · cited by 233
- two_mulproof · cited by 232
- dist_commproof · cited by 188
- EuclideanGeometry.Sphere.centerproof · cited by 181
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_wbtwproof · cited by 2