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 wbit_or_other : forall sz sz' (n1 n2 : word sz'), (wordToNat n1 < sz)%nat
-> (wordToNat n2 < sz)%nat
-> (n1 <> n2)
-> (wbit sz n1) ^& (wbit sz n2) = wzero sz.