EuclideanGeometry.Sphere.mem_coe
∀ {P : Type u_2} [inst : MetricSpace P] {p : P} {s : EuclideanGeometry.Sphere P},
p ∈ Metric.sphere s.center s.radius ↔ p ∈ s- Defined in
- Mathlib.Geometry.Euclidean.Sphere.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- MetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- MetricSpacestatement and proof · cited by 1,684
- Metric.spherestatement · cited by 371
- EuclideanGeometry.Spherestatement and proof · cited by 233
- EuclideanGeometry.Sphere.centerstatement · cited by 181
- EuclideanGeometry.Sphere.radiusstatement · cited by 123
Cited by2
Results whose statement or proof uses this declaration.
- EuclideanGeometry.dist_of_mem_subset_sphereproof · cited by 2
- EuclideanGeometry.existsUnique_dist_eq_of_insertproof · cited by 1