Theorems · Theorem · functional analysis

dist_center_homothety

∀ {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),
  dist p₁ ((AffineMap.homothety p₁ c) p₂) = ‖c‖ * dist p₁ p₂

Defined in

Mathlib.Analysis.Normed.Affine.AddTorsor

Cited by

2 results in Mathlib

Foundations

Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SeminormedAddCommGroupPseudoMetricSpaceNormedAddTorsorNormedFieldNormedSpace