∀ {C : Type u_3} [inst : CategoryTheory.Category.{u_2, u_3} C] {F : CategoryTheory.Functor Cᵒᵖ (Type u_1)} {X : Cᵒᵖ}
  (x : F.obj X) {U V : Cᵒᵖ} (g : U ⟶ V), {u | ∃ f, F.map f x = u} ⊆ F.map g ⁻¹' {u | ∃ f, F.map f x = u}