Definition Bag_of_Data := Site -> Site -> queue Data.(* This is taken straight from Jean's file *)

Definition Post_message (m0 : Message) (b0 : Bag_of_message)
  (s0 s1 : Site) :=
  change_queue (queue Message) b0 s0 s1 (input Message m0 (b0 s0 s1)).Definition Collect_message (b0 : Bag_of_message) (s0 s1 : Site) :=
  change_queue (queue Message) b0 s0 s1 (first_out Message (b0 s0 s1)).

Lemma collect_elsewhere : forall (b0 : Bag_of_message) (s0 s1 s2 s3 : Site), s0 <> s2 \/ s1 <> s3 -> Collect_message b0 s0 s1 s2 s3 = b0 s2 s3.