Isometry.cospherical
∀ {E : Type u_3} {F : Type u_4} [inst : MetricSpace E] [inst_1 : MetricSpace F] {f : E → F},
Isometry f → ∀ {ps : Set E}, EuclideanGeometry.Cospherical ps → EuclideanGeometry.Cospherical (f '' ps)If ps is cospherical, then any of its isometric images is cospherical.
- Defined in
- Mathlib.Geometry.Euclidean.Sphere.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MetricSpaceMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realproof · cited by 25,697
- Set.imagestatement and proof · cited by 5,609
- MetricSpacestatement and proof · cited by 1,684
- Dist.distproof · cited by 1,539
- Isometrystatement and proof · cited by 230
- EuclideanGeometry.Cosphericalstatement and proof · cited by 39
- Isometry.dist_eqproof · cited by 21
Cited by2
Results whose statement or proof uses this declaration.
- EuclideanGeometry.Cospherical.subtype_valproof · cited by 2
- EuclideanGeometry.Cospherical.inclusionproof · cited by 0