destruct sz; simpl.
rewrite (shatter_word x); reflexivity.
rewrite roundTrip_0; simpl.
rewrite plus_0_r.
rewrite (shatter_word x).
f_equal.
apply mod2_WS.
rewrite div2_WS.
apply natToWord_wordToNat.
Qed.

Theorem wmult_comm : forall sz (x y : word sz), x ^* y = y ^* x.
intros; repeat rewrite wmult_alt; unfold wmultN, wordBinN; auto with arith.