∀ {X : Type u_1} {α : Type u_2} {s : Set X} {f g : X → α} (motive : (∃ x, s.restrict f x = s.restrict g x) → Prop)
  (x : ∃ x, s.restrict f x = s.restrict g x), (∀ (x : ↑s) (hx : s.restrict f x = s.restrict g x), motive ⋯) → motive x