Theorems · Theorem · geometry

AffineIsometryEquiv.pointReflection_fixed_iff

∀ {𝕜 : Type u_1} {V : Type u_2} {P : Type u_10} [inst : NormedField 𝕜] [inst_1 : SeminormedAddCommGroup V]
  [inst_2 : NormedSpace 𝕜 V] [inst_3 : PseudoMetricSpace P] [inst_4 : NormedAddTorsor V P] [Invertible 2] {x y : P},
  (AffineIsometryEquiv.pointReflection 𝕜 x) y = y ↔ y = x

Defined in

Mathlib.Analysis.Normed.Affine.Isometry

Cited by

1 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Quot.sound

Assumes

NormedFieldSeminormedAddCommGroupNormedSpacePseudoMetricSpaceNormedAddTorsorInvertible