∀ {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]
  {s : Set α} [hs : s.OrdConnected] {f : α → δ},
  ContinuousOn f s → ∀ {a b : α}, a ∈ s → b ∈ s → Set.SurjOn f s (Set.Icc (f a) (f b))