AffineIsometryEquiv.dist_pointReflection_self_real
∀ {V : Type u_2} {P : Type u_10} [inst : SeminormedAddCommGroup V] [inst_1 : PseudoMetricSpace P]
[inst_2 : NormedAddTorsor V P] [inst_3 : NormedSpace ℝ V] (x y : P),
dist ((AffineIsometryEquiv.pointReflection ℝ x) y) y = 2 * dist x y- Defined in
- Mathlib.Analysis.Normed.Affine.Isometry
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
- AffineIsometryEquivstatement · cited by 118
- AffineIsometryEquiv.pointReflectionstatement · cited by 14
- Real.norm_twoproof · cited by 4
- AffineIsometryEquiv.dist_pointReflection_selfproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsometryEquiv.midpoint_fixedproof · cited by 1