∀ {F : Type u_6} {α : outParam (Type u_7)} {β : outParam (Type u_8)} [inst : TopologicalSpace α] [inst_1 : Preorder α]
  [inst_2 : TopologicalSpace β] [inst_3 : Preorder β] [inst_4 : FunLike F α β]
  [toContinuousOrderHomClass : ContinuousOrderHomClass F α β],
  (∀ (f : F) ⦃a : α⦄ ⦃b : β⦄, f a ≤ b → ∃ c, a ≤ c ∧ f c = b) → EsakiaHomClass F α β