Theorems · Theorem · geometry

EuclideanGeometry.Sphere.inter_orthRadius_eq_empty_of_finrank_eq_one

∀ {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 : P},
  p ≠ s.center →
    dist p s.center ≠ s.radius → Module.finrank ℝ V = 1 → Metric.sphere s.center s.radius ∩ ↑(s.orthRadius p) = ∅

Defined in

Mathlib.Geometry.Euclidean.Sphere.OrthRadius

Cited by

1 results in Mathlib

Foundations

Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor