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Theorems · Theorem · geometry

AffineIsometryEquiv.pointReflection_self

∀ {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] (x : P),
  (AffineIsometryEquiv.pointReflection 𝕜 x) x = x
Defined in
Mathlib.Analysis.Normed.Affine.Isometry
Cited by
2 results in Mathlib
Foundations
Depth 51 from the axioms · uses propext, Quot.sound
Assumes
NormedFieldSeminormedAddCommGroupNormedSpacePseudoMetricSpaceNormedAddTorsor
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AffineIsometryEquiv.dist_pointReflection_fixed · cited by 1AffineIsometryEquiv.dist_…IsometryEquiv.map_midpoint · cited by 0IsometryEquiv.map_midpointDFunLike.coe · cited by 62936DFunLike.coeNormedSpace · cited by 12499NormedSpaceSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupPseudoMetricSpace · cited by 1550PseudoMetricSpaceNormedAddTorsor · cited by 1325NormedAddTorsorNormedField · cited by 1084NormedFieldAffineIsometryEquiv · cited by 118AffineIsometryEquivAffineIsometryEquiv.pointReflection · cited by 14AffineIsometryEquiv.point…AffineEquiv.pointReflection_self · cited by 5AffineEquiv.pointReflecti…AffineIsometryEquiv.pointRefl…CITED BYCITES

Cites9

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Cited by2

Results whose statement or proof uses this declaration.