∀ {X Y Z : AddCommMonCat} (f : X ⟶ Y) (g : Y ⟶ Z),
  AddCommMonCat.ofHom
      (AddEquiv.ulift.symm.toAddMonoidHom.comp
        ((AddCommMonCat.Hom.hom (CategoryTheory.CategoryStruct.comp f g)).comp AddEquiv.ulift.toAddMonoidHom)) =
    CategoryTheory.CategoryStruct.comp
      (AddCommMonCat.ofHom
        (AddEquiv.ulift.symm.toAddMonoidHom.comp ((AddCommMonCat.Hom.hom f).comp AddEquiv.ulift.toAddMonoidHom)))
      (AddCommMonCat.ofHom
        (AddEquiv.ulift.symm.toAddMonoidHom.comp ((AddCommMonCat.Hom.hom g).comp AddEquiv.ulift.toAddMonoidHom)))