∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] [inst_1 : ConditionallyCompleteLinearOrder β]
  [inst_2 : TopologicalSpace β] [OrderTopology β] {f : α → β},
  Monotone f →
    ∀ {x : α} [inst_4 : TopologicalSpace α] [OrderTopology α],
      nhdsWithin x (Set.Iio x) ≠ ⊥ → Function.leftLim f x = sSup (f '' Set.Iio x)