∀ {α : Type u_2} {β : Type u_3} [inst : OmegaCompletePartialOrder α] [inst_1 : OmegaCompletePartialOrder β] (f : α → β),
  OmegaCompletePartialOrder.ωScottContinuous f = ScottContinuousOn (Set.range fun c => Set.range ⇑c) f