intros n x; induction x as [|a x IHx]; intros.
- norm.
- simpl Nwscal.
repeat rewrite gen_phiNword_cons.
rewrite (fun sreq => gen_phiN_mult Rsth sreq (ARth_SRth ARth))
by (destruct Reqe; constructor; trivial).
rewrite IHx.
norm.
Qed.

(* Specifications: *)
Lemma Nwmul_ok : forall x y,
gen_phiNword (Nwmul x y) == gen_phiNword x * gen_phiNword y.