∀ {α : Type u_2} {β : Type u_3} [inst : ConditionallyCompleteLinearOrder α] [inst_1 : TopologicalSpace α]
  [OrderTopology α] [inst_3 : TopologicalSpace β] [DenselyOrdered α] [inst_5 : ConditionallyCompleteLinearOrder β]
  [OrderTopology β] {f : α → β} {a b : α},
  a ≤ b → ContinuousOn f (Set.Icc a b) → AntitoneOn f (Set.Icc a b) → f '' Set.Icc a b = Set.Icc (f b) (f a)