∀ {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} [self : EsakiaHomClass F α β] (f : F)
  ⦃a : α⦄ ⦃b : β⦄, f a ≤ b → ∃ c, a ≤ c ∧ f c = b