EuclideanGeometry.Sphere.IsTangentAt.mem_sphere
∀ {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 : P} {as : AffineSubspace ℝ P},
s.IsTangentAt p as → p ∈ s- Cited by
- 6 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- 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
- NormedAddTorsorstatement and proof · cited by 1,325
- AffineSubspacestatement and proof · cited by 871
- EuclideanGeometry.Spherestatement and proof · cited by 233
- EuclideanGeometry.Sphere.IsTangentAtstatement and proof · cited by 35
Cited by6
Results whose statement or proof uses this declaration.
- EuclideanGeometry.Sphere.IsTangentAt.dist_sq_eq_of_memproof · cited by 6
- EuclideanGeometry.Sphere.IsTangent.infDist_eq_radiusproof · cited by 2
- EuclideanGeometry.Sphere.IsTangentAt.mem_and_mem_iff_eqproof · cited by 1
- EuclideanGeometry.Sphere.IsTangentAt.eq_orthRadius_of_finrank_add_one_eqproof · cited by 1
- EuclideanGeometry.Sphere.isTangentAt_orthRadius_iff_memproof · cited by 1
- EuclideanGeometry.Sphere.IsTangentAt.radius_lt_dist_centerproof · cited by 0