Definition no_message (c : Config) :=
forall s1 s2 : Site, In s1 LS -> In s2 LS -> bm c s1 s2 = empty Message.

Lemma exist_non_empty_queue :
forall c : Config,
legal c ->
~ no_message c ->
exists s1 : Site,
(exists s2 : Site, s1 <> s2 /\ bm c s1 s2 <> empty Message).