∀ {C : Type u_3} [inst : CategoryTheory.Category.{u_2, u_3} C] {F : CategoryTheory.Functor C (Type u_1)}
  (x : Set (CategoryTheory.Subfunctor F)) (x_1 : CategoryTheory.Subfunctor F),
  (∀ b ∈ x, x_1 ≤ b) →
    ∀ (x_3 : C), ∀ x_4 ∈ x_1.obj x_3, x_4 ∈ { obj := fun U => sInf ((fun T => T.obj U) '' x), map := ⋯ }.obj x_3