intro.
rewrite (shatter_word a).
replace (wtl a) with WO by auto.
destruct (whd a).
right; apply eq_refl.
left; apply eq_refl.
Defined.

Lemma induct_word_S: forall (P : forall n : nat, word (S n) -> Prop),
(forall b, P 0 (WS b WO)) ->
(forall b b0 n (w : word n), P n (WS b0 w) -> P (S n) (WS b (WS b0 w))) ->
forall (n : nat) (w : word (S n)), P n w.