induction n as [n] using strong; intros.
destruct n; simpl in *.
elimtype False; omega.
destruct n; simpl in *; auto.
destruct k as [|k]; simpl in *.
discriminate.
apply H with k; auto.
Qed.

(* Specifications: *)
Theorem wzero'_def : forall sz, wzero' sz = wzero sz.
unfold wzero; induction sz; simpl; intuition.