∀ {α : Type u_2} {β : Type u_1} [inst : Preorder β] {f : α → β} {a : α} (motive : (∃ x, f a ≤ x ∧ x < f a) → Prop)
  (x : ∃ x, f a ≤ x ∧ x < f a), (∀ (_y : β) (hy : f a ≤ _y ∧ _y < f a), motive ⋯) → motive x