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).