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_same : forall sz sz' (n : word sz'), (wordToNat n < sz)%nat
-> (wbit sz n) ^| (wbit sz n) <> wzero sz.