∀ {α : Type u_2} {β : Type u_1} {s : Set α} (a x : β) (motive : x ∈ (fun x => a) '' s → Prop)
  (x_1 : x ∈ (fun x => a) '' s), (∀ (w : α) (left : w ∈ s) (h : (fun x => a) w = x), motive ⋯) → motive x_1