∀ {J : Type u_1} [inst : CategoryTheory.SmallCategory J] (j : J) {i j_1 : J} {f : i ⟶ j_1},
  CategoryTheory.MorphismProperty.ofHoms (fun x => CategoryTheory.CategoryStruct.id j) f →
    CategoryTheory.ObjectProperty.ofObj (fun x => j) j_1