EuclideanGeometry.Sphere.IsTangentAt.mem_and_mem_iff_eq
∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : MetricSpace P]
[inst_3 : NormedAddTorsor V P] {s : EuclideanGeometry.Sphere P} {p q : P} {as : AffineSubspace ℝ P},
s.IsTangentAt p as → (q ∈ s ∧ q ∈ as ↔ q = p)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- InnerProductSpacestatement and proof · cited by 3,523
- MetricSpacestatement and proof · cited by 1,684
- Dist.distproof · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
- AffineSubspacestatement and proof · cited by 871
- EuclideanGeometry.Spherestatement and proof · cited by 233
- EuclideanGeometry.Sphere.centerproof · cited by 181
- EuclideanGeometry.Sphere.radiusproof · cited by 123
- EuclideanGeometry.Sphere.IsTangentAtstatement and proof · cited by 35
- EuclideanGeometry.Sphere.IsTangentAt.mem_sphereproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanGeometry.Sphere.IsTangentAt.eq_of_mem_of_memproof · cited by 1