Theorems · Theorem · geometry

EuclideanGeometry.Sphere.nonempty_iff

∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [NormedSpace ℝ V] [inst_2 : MetricSpace P]
  [NormedAddTorsor V P] [Nontrivial V] {s : EuclideanGeometry.Sphere P},
  (Metric.sphere s.center s.radius).Nonempty ↔ 0 ≤ s.radius

Defined in

Mathlib.Geometry.Euclidean.Sphere.Basic

Cited by

1 results in Mathlib

Foundations

Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMetricSpaceNormedAddTorsorNontrivial