∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLinearOrder α] [inst_1 : TopologicalSpace α] [OrderTopology α]
  [inst_3 : CompleteLinearOrder β] [inst_4 : TopologicalSpace β] [OrderClosedTopology β] {f : α → β} {s : Set α},
  ContinuousAt f (sInf s) → Antitone f → f ⊤ = ⊥ → f (sInf s) = sSup (f '' s)