intros x; induction x as [|n x IHx]; intros y.
- simpl.
norm.
- destruct y.
+ simpl Nwadd; norm.
+ simpl Nwadd.
repeat rewrite gen_phiNword_cons.
rewrite (fun sreq => gen_phiN_add Rsth sreq (ARth_SRth ARth)) by
(destruct Reqe; constructor; trivial).
rewrite IHx.
norm.
add_push (- gen_phiNword x); reflexivity.
Qed.

Lemma Nwopp_ok : forall x, gen_phiNword (Nwopp x) == - gen_phiNword x.
simpl.