∀ {α : Type uα} [inst : UniformSpace α] (pkg : AbstractCompletion.{vα, uα} α) {β : Type uβ} [inst_1 : UniformSpace β]
  (pkg' : AbstractCompletion.{vβ, uβ} β) {f : α → β},
  UniformContinuous f → ∀ (a : α), pkg.map pkg' f (pkg.coe a) = pkg'.coe (f a)