∀ {α : Sort u_3} {β : Sort u_2} {γ : Sort u_1} {f : α → β} {g : γ → α} (a : α)
  (motive : (∃ a_1, (f ∘ g) a_1 = f a) → Prop) (x : ∃ a_1, (f ∘ g) a_1 = f a),
  (∀ (c : γ) (hc : (f ∘ g) c = f a), motive ⋯) → motive x