Instance ARsub_ext : Proper (req ==> req ==> req) rsub.Ltac mrewrite :=
   repeat first
     [ rewrite (ARadd_0_l ARth)
     | rewrite <- ((ARadd_comm ARth) 0)
     | rewrite (ARmul_1_l ARth)
     | rewrite <- ((ARmul_comm ARth) 1)
     | rewrite (ARmul_0_l ARth)
     | rewrite <- ((ARmul_comm ARth) 0)
     | rewrite (ARdistr_l ARth)
     | reflexivity
     | match goal with
       | |- context [?z * (?x + ?y)] => rewrite ((ARmul_comm ARth) z (x+y))
       end].

Lemma ARadd_assoc2 x y z : (y + x) + z == (y + z) + x.