∀ {α : Type ua} {β : Type ub} [inst : UniformSpace α] [inst_1 : UniformSpace β] {p : α → Prop} {q : β → Prop}
  {f : α → β}, UniformContinuous f → ∀ (h : ∀ (x : α), p x → q (f x)), UniformContinuous (Subtype.map f h)