Theorems · Theorem · geometry

EuclideanGeometry.Sphere.secondInter_mem

∀ {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), s.secondInter p v ∈ s ↔ p ∈ s

The point given by secondInter lies on the sphere.

Defined in

Mathlib.Geometry.Euclidean.Sphere.SecondInter

Cited by

3 results in Mathlib

Foundations

Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor