intros x; induction x as [|a x IHx]; intros.
- norm.
- destruct a.
+ simpl Nwmul.
rewrite Nwopp_ok.
rewrite IHx.
rewrite gen_phiNword_cons.
norm.
+ simpl Nwmul.
unfold Nwsub.
rewrite Nwadd_ok.
rewrite Nwscal_ok.
rewrite Nwopp_ok.
rewrite IHx.
rewrite gen_phiNword_cons.
norm.
Qed.

(* Proof that [.] satisfies morphism specifications *)
Lemma gen_phiNword_morph :
ring_morph 0 1 radd rmul rsub ropp req
NwO NwI Nwadd Nwmul Nwsub Nwopp Nweq_bool gen_phiNword.