EuclideanGeometry.mem_sphere
∀ {P : Type u_2} [inst : MetricSpace P] {p : P} {s : EuclideanGeometry.Sphere P}, p ∈ s ↔ dist p s.center = s.radius- Defined in
- Mathlib.Geometry.Euclidean.Sphere.Basic
- Cited by
- 22 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.
- Realstatement · cited by 25,697
- MetricSpacestatement and proof · cited by 1,684
- Dist.diststatement · cited by 1,539
- EuclideanGeometry.Spherestatement and proof · cited by 233
- EuclideanGeometry.Sphere.centerstatement · cited by 181
- EuclideanGeometry.Sphere.radiusstatement · cited by 123
Cited by22
Results whose statement or proof uses this declaration.
- EuclideanGeometry.Sphere.IsDiameter.right_memproof · cited by 7
- EuclideanGeometry.dist_center_eq_dist_center_of_mem_sphereproof · cited by 3
- EuclideanGeometry.Sphere.IsDiameter.dist_left_rightproof · cited by 3
- EuclideanGeometry.inner_pos_or_eq_of_dist_le_radiusproof · cited by 3
- EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_wbtwproof · cited by 2
- EuclideanGeometry.dist_of_mem_subset_sphereproof · cited by 2
- EuclideanGeometry.Sphere.dist_div_cos_oangle_center_div_two_eq_radiusproof · cited by 2
- EuclideanGeometry.Sphere.mul_dist_eq_abs_powerproof · cited by 2
- Affine.Simplex.faceOppositeCentroid_mem_ninePointCircleproof · cited by 2
- EuclideanGeometry.existsUnique_dist_eq_of_insertproof · cited by 1
- EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_distproof · cited by 1