EuclideanGeometry.dist_reflection
∀ {𝕜 : Type u_1} {V : Type u_2} {P : Type u_3} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup V]
[inst_2 : InnerProductSpace 𝕜 V] [inst_3 : MetricSpace P] [inst_4 : NormedAddTorsor V P] (s : AffineSubspace 𝕜 P)
[inst_5 : Nonempty ↥s] [inst_6 : s.direction.HasOrthogonalProjection] (p₁ p₂ : P),
dist p₁ ((EuclideanGeometry.reflection s) p₂) = dist ((EuclideanGeometry.reflection s) p₁) p₂The distance between p₁ and the reflection of p₂ equals that
between the reflection of p₁ and p₂.
- Defined in
- Mathlib.Geometry.Euclidean.Projection
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- MetricSpacestatement and proof · cited by 1,684
- Dist.diststatement and proof · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
- AffineSubspacestatement and proof · cited by 871
- AffineSubspace.directionstatement and proof · cited by 339
- Submodule.HasOrthogonalProjectionstatement and proof · cited by 245
- AffineIsometryEquivstatement · cited by 118
Cited by1
Results whose statement or proof uses this declaration.
- Affine.Triangle.dist_circumcenter_reflection_orthocenterproof · cited by 1