Theorems · Theorem · geometry

EuclideanGeometry.Sphere.secondInter_smul

∀ {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) (v : V) {r : ℝ},
  r ≠ 0 → s.secondInter p (r • v) = s.secondInter p v

secondInter is unchanged by multiplying the vector by a nonzero real.

Defined in

Mathlib.Geometry.Euclidean.Sphere.SecondInter

Cited by

2 results in Mathlib

Foundations

Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor