∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] [inst_1 : TopologicalSpace α] [OrderTopology α]
  [inst_3 : LinearOrder β] [inst_4 : TopologicalSpace β] [OrderTopology β] [DenselyOrdered β] {f : α → β} {s : Set α}
  {a : α},
  StrictMonoOn f s →
    s ∈ nhdsWithin a (Set.Ici a) → f '' s ∈ nhdsWithin (f a) (Set.Ici (f a)) → ContinuousWithinAt f (Set.Ici a) a