destruct b; simpl.
rewrite untimes2.
case_eq (2 * wordToNat x); intuition.
eapply mod2_S; eauto.
rewrite <- (mod2_double (wordToNat x)); f_equal; omega.
Qed.

Theorem div2_WS : forall sz (x : word sz) b, div2 (wordToNat (WS b x)) = wordToNat x.
destruct b; rewrite wordToNat_wordToNat'; unfold wordToNat'; fold wordToNat'.