EuclideanGeometry.Sphere.IsTangentAt.eq_of_mem_of_mem
∀ {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 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- EuclideanGeometry.Sphere.IsTangentAt.mem_and_mem_iff_eqproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Affine.Simplex.ExcenterExists.touchpoint_notMem_affineSpan_of_neproof · cited by 2