intros sz a b c H.
apply (f_equal (fun x => x ^+ ^~ c)) in H.
repeat rewrite <- wplus_assoc in H.
rewrite wminus_inv in H.
repeat rewrite (wplus_comm _ (wzero sz)) in H.
repeat rewrite wplus_unit in H.
assumption.
Qed.

Lemma wplus_one_neq: forall {sz} (w: word (S sz)), w ^+ (natToWord (S sz) 1) <> w.