EuclideanGeometry.Sphere.IsTangentAt.radius_lt_dist_center
∀ {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} {as : AffineSubspace ℝ P} {p q : P},
s.IsTangentAt p as → q ∈ as → q ≠ p → s.radius < dist q s.center- Cited by
- 0 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
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.diststatement and proof · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
- AffineSubspacestatement and proof · cited by 871
- abs_of_nonnegproof · cited by 279
- EuclideanGeometry.Spherestatement and proof · cited by 233
- EuclideanGeometry.Sphere.centerstatement and proof · cited by 181
- EuclideanGeometry.Sphere.radiusstatement and proof · cited by 123
- EuclideanGeometry.Sphere.IsTangentAtstatement and proof · cited by 35
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