∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  [inst_2 : CategoryTheory.Limits.HasCokernels C] (X : C) (P Q : CategoryTheory.Subobject X),
  P ≤ Q →
    CategoryTheory.Subobject.lift (fun x f x_1 => CategoryTheory.Subobject.mk (CategoryTheory.Limits.cokernel.π f).op) ⋯
        P ≤
      CategoryTheory.Subobject.lift (fun x f x_1 => CategoryTheory.Subobject.mk (CategoryTheory.Limits.cokernel.π f).op)
        ⋯ Q