∀ {α : Type u_1} [inst : LE α] {s : Set α} (motive : (IsDirected ↑s fun x1 x2 => x1 ≤ x2) → Prop)
  (x : IsDirected ↑s fun x1 x2 => x1 ≤ x2), (∀ (h : ∀ (a b : ↑s), ∃ c, a ≤ c ∧ b ≤ c), motive ⋯) → motive x