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 wmult_plus_distr_l: forall (sz : nat) (x y z : word sz),
z ^* (x ^+ y) = z ^* x ^+ z ^* y.