Theorems · Theorem · geometry

AffineIsometry.map_vadd

∀ {𝕜 : Type u_1} {V : Type u_2} {V₂ : Type u_5} {P : Type u_10} {P₂ : Type u_11} [inst : NormedField 𝕜]
  [inst_1 : SeminormedAddCommGroup V] [inst_2 : NormedSpace 𝕜 V] [inst_3 : PseudoMetricSpace P]
  [inst_4 : NormedAddTorsor V P] [inst_5 : SeminormedAddCommGroup V₂] [inst_6 : NormedSpace 𝕜 V₂]
  [inst_7 : PseudoMetricSpace P₂] [inst_8 : NormedAddTorsor V₂ P₂] (f : P →ᵃⁱ[𝕜] P₂) (p : P) (v : V),
  f (v +ᵥ p) = f.linearIsometry v +ᵥ f p

Defined in

Mathlib.Analysis.Normed.Affine.Isometry

Cited by

6 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Quot.sound

Assumes

NormedFieldSeminormedAddCommGroupNormedSpacePseudoMetricSpaceNormedAddTorsorSeminormedAddCommGroupNormedSpacePseudoMetricSpaceNormedAddTorsor