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