Fixpoint countLeadingZerosWord_nat ni: word ni -> nat :=
match ni return word ni -> nat with
| 0 => fun _ => 0
| S m => fun e =>
if (weq (split2 m 1 (nat_cast (fun n => word n) (eq_sym (Nat.add_1_r m)) e)) WO~0)
then 1 + @countLeadingZerosWord_nat m (split1 m 1 (nat_cast (fun n => word n) (eq_sym (Nat.add_1_r m)) e))
else 0
end.

Lemma sext0: forall sz0 sz (v: word sz) (e: sz0 = 0),
sext v sz0 = nat_cast word (eq_ind_r (fun sz0 : nat => sz = sz + sz0) (plus_n_O sz) e) v.