∀ {α : Type uα} [inst : UniformSpace α] (pkg : AbstractCompletion.{vα, uα} α) {β : Type uβ} [inst_1 : UniformSpace β]
  (pkg' : AbstractCompletion.{vβ, uβ} β) {γ : Type uγ} [inst_2 : UniformSpace γ] (f : α → β → γ),
  pkg.extend₂ pkg' f = Function.curry ((pkg.prod pkg').extend (Function.uncurry f))