Theorems · Theorem · geometry

EuclideanGeometry.Cospherical.subtype_val

∀ {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 : AffineSubspace ℝ P} [Nonempty ↥S] {ps : Set ↥S},
  EuclideanGeometry.Cospherical ps → EuclideanGeometry.Cospherical (Subtype.val '' ps)

If a set of points in an affine subspace is cospherical, then its image under the coercion to the ambient space is cospherical.

Defined in

Mathlib.Geometry.Euclidean.Sphere.Basic

Cited by

2 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupNormedSpaceMetricSpaceNormedAddTorsorNonempty