∀ {α : Type u_1} {β : Type u_3} {γ : Type u_2} [inst : TopologicalSpace α] [inst_1 : Preorder α]
  [inst_2 : TopologicalSpace β] [inst_3 : Preorder β] [inst_4 : TopologicalSpace γ] [inst_5 : Preorder γ]
  (g : EsakiaHom β γ) (f : EsakiaHom α β) (a : α) (b : γ),
  (g.comp f.toContinuousOrderHom).toFun a ≤ b → ∃ c, a ≤ c ∧ (g.comp f.toContinuousOrderHom).toFun c = b