Local Arguments nat_cast: simpl never.

Lemma sext_combine: (* Note: not axiom free *)
forall sz n (w: word (sz + n)) sz1 (w1: word sz1)
sz2 (Hsz2: sz2 <> 0) (w2: word sz2),
existT word _ w = existT word _ (combine w1 (sext w2 n)) ->
exists sw, w = sext sw n /\ existT word _ sw = existT word _ (combine w1 w2).