∀ {α : Type u_2} {β : Type u_3} [inst : CompletePartialOrder α] [inst_1 : Preorder β] {f : α → β},
  ScottContinuous f ↔ ∀ ⦃d : Set α⦄, d.Nonempty → DirectedOn (fun x1 x2 => x1 ≤ x2) d → IsLUB (f '' d) (f (sSup d))