∀ {G : Type u_1} [inst : Group G] (X : Type u_1) (of : X → G)
  (h : ∀ {H : Type u_1} [inst_1 : Group H] (f : X → H), ∃! F, ∀ (a : X), F (of a) = f a) {H : Type u_1}
  [inst_1 : Group H] (f : X → H), ⇑(Classical.choose ⋯) ∘ of = f