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

Theorem zero_or_wordToNat_S: forall sz (n : word sz),
n = $0 \/
exists nn, wordToNat n = S nn /\ wordToNat (n ^- $1) = nn.