∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : CommMonoid α] [inst_1 : TopologicalSpace α] {g : γ → β}
  (f : β → α) {s : Set γ}, Set.InjOn g s → ∏' (x : ↑(g '' s)), f ↑x = ∏' (x : ↑s), f (g ↑x)