EuclideanGeometry.dist_center_eq_dist_center_of_mem_sphere
∀ {P : Type u_2} [inst : MetricSpace P] {p₁ p₂ : P} {s : EuclideanGeometry.Sphere P},
p₁ ∈ s → p₂ ∈ s → dist p₁ s.center = dist p₂ s.center- Defined in
- Mathlib.Geometry.Euclidean.Sphere.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- MetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- MetricSpacestatement and proof · cited by 1,684
- Dist.diststatement and proof · cited by 1,539
- EuclideanGeometry.Spherestatement and proof · cited by 233
- EuclideanGeometry.Sphere.centerstatement and proof · cited by 181
- EuclideanGeometry.Sphere.radiusproof · cited by 123
- EuclideanGeometry.mem_sphereproof · cited by 22
Cited by3
Results whose statement or proof uses this declaration.
- EuclideanGeometry.inner_vsub_vsub_of_mem_sphere_of_mem_sphereproof · cited by 0
- EuclideanGeometry.Sphere.inner_vsub_center_midpoint_vsubproof · cited by 0