Theorems · Theorem · geometry

EuclideanGeometry.Sphere.IsTangent.notMem_of_dist_lt

∀ {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},
  s.IsTangent as → ∀ {p : P}, dist p s.center < s.radius → p ∉ as

Defined in

Mathlib.Geometry.Euclidean.Sphere.Tangent

Cited by

1 results in Mathlib

Foundations

Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor