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 combine_ge sz1 sz2 (x1 y1: word sz1) (x2 y2: word sz2):
(combine x1 x2 <= combine y1 y2 ->
x2 < y2 \/ (x2 = y2 /\ x1 <= y1))%word.