Theorems · Theorem · functional analysis

nndist_homothety_self

∀ {V : Type u_1} {P : Type u_2} [inst : SeminormedAddCommGroup V] [inst_1 : PseudoMetricSpace P]
  [inst_2 : NormedAddTorsor V P] {𝕜 : Type u_5} [inst_3 : NormedField 𝕜] [inst_4 : NormedSpace 𝕜 V] (p₁ p₂ : P) (c : 𝕜),
  nndist ((AffineMap.homothety p₁ c) p₂) p₂ = ‖1 - c‖₊ * nndist p₁ p₂

Defined in

Mathlib.Analysis.Normed.Affine.AddTorsor

Cited by

0 results in Mathlib

Foundations

Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SeminormedAddCommGroupPseudoMetricSpaceNormedAddTorsorNormedFieldNormedSpace