EuclideanGeometry.Sphere.center_ne_iff_ne_of_mem
∀ {P : Type u_2} [inst : MetricSpace P] {s₁ s₂ : EuclideanGeometry.Sphere P} {p : P},
p ∈ s₁ → p ∈ s₂ → (s₁.center ≠ s₂.center ↔ s₁ ≠ s₂)- Defined in
- Mathlib.Geometry.Euclidean.Sphere.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext
- Assumes
- MetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MetricSpacestatement and proof · cited by 1,684
- Iff.notproof · cited by 489
- EuclideanGeometry.Spherestatement and proof · cited by 233
- EuclideanGeometry.Sphere.centerstatement · cited by 181
- EuclideanGeometry.Sphere.center_eq_iff_eq_of_memproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- EuclideanGeometry.eq_of_mem_sphere_of_mem_sphere_of_finrank_eq_twoproof · cited by 1