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