Theorems · Theorem · geometry

EuclideanGeometry.Sphere.IsDiameter.left_ne_right_iff_radius_ne_zero

∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : NormedSpace ℝ V] [inst_2 : MetricSpace P]
  [inst_3 : NormedAddTorsor V P] {s : EuclideanGeometry.Sphere P} {p₁ p₂ : P},
  s.IsDiameter p₁ p₂ → (p₁ ≠ p₂ ↔ s.radius ≠ 0)

Defined in

Mathlib.Geometry.Euclidean.Sphere.Basic

Cited by

2 results in Mathlib

Foundations

Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMetricSpaceNormedAddTorsor