∀ {α : Type u} [inst : ConditionallyCompleteLinearOrder α] [inst_1 : TopologicalSpace α] [OrderTopology α]
  [DenselyOrdered α] {δ : Type u_1} [inst_4 : LinearOrder δ] [inst_5 : TopologicalSpace δ] [OrderClosedTopology δ]
  {a b : α} {f : α → δ},
  a ≤ b →
    ContinuousOn f (Set.Icc a b) →
      Set.InjOn f (Set.Icc a b) → StrictMonoOn f (Set.Icc a b) ∨ StrictAntiOn f (Set.Icc a b)