∀ {X : Type u_1} {Y : Type u_2} [inst : PseudoEMetricSpace X] [inst_1 : PseudoEMetricSpace Y] {r : NNReal} {f : X → Y}
  {C D s : NNReal}, (∀ (x y : X), edist x y ≤ ↑D) → HolderWith C r f → s ≤ r → HolderWith (C * D ^ (↑r - ↑s)) s f