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 wmul_mod_distr_does_not_hold: ~ forall sz (a b n: word sz),
n <> $0 ->
(a ^* b) ^% n = ((a ^% n) ^* (b ^% n)) ^% n.