EuclideanGeometry.Sphere.center_mem_orthRadius_iff
∀ {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} {p : P}, s.center ∈ s.orthRadius p ↔ p = s.center- Cited by
- 1 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.
Cites15
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
- NormedAddTorsorstatement and proof · cited by 1,325
- Inner.innerproof · cited by 1,089
- AffineSubspacestatement · cited by 871
- VSub.vsubproof · cited by 817
- EuclideanGeometry.Spherestatement and proof · cited by 233
- EuclideanGeometry.Sphere.centerstatement and proof · cited by 181
- neg_vsub_eq_vsub_revproof · cited by 87
- inner_self_eq_norm_sq_to_Kproof · cited by 72
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanGeometry.Sphere.isTangent_orthRadius_iff_memproof · cited by 1