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 ARopp_mul_r x y : - (x * y) == x * -y.