EuclideanGeometry.dist_of_mem_subset_mk_sphere
∀ {P : Type u_2} [inst : MetricSpace P] {p c : P} {ps : Set P} {r : ℝ},
p ∈ ps → ps ⊆ Metric.sphere { center := c, radius := r }.center { center := c, radius := r }.radius → dist p c = r- Defined in
- Mathlib.Geometry.Euclidean.Sphere.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- MetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- MetricSpacestatement and proof · cited by 1,684
- Dist.diststatement · cited by 1,539
- Metric.spherestatement and proof · cited by 371
- EuclideanGeometry.Sphere.centerstatement and proof · cited by 181
- EuclideanGeometry.Sphere.radiusstatement and proof · cited by 123
- EuclideanGeometry.dist_of_mem_subset_sphereproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanGeometry.existsUnique_dist_eq_of_insertproof · cited by 1