Proof using .
clear. intros.
rewrite <- (natToWord_wordToNat w1) at 1.
rewrite <- (natToWord_wordToNat w2) at 1.
rewrite <- natToWord_mult.
rewrite wordToNat_natToWord_eqn.
reflexivity.
Qed.

Lemma wor_r_wzero_1 sz: (* Note: not axiom free *)
forall w1 w2,
w1 ^| w2 = natToWord sz 0 ->
w2 = natToWord sz 0.