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 in_collect : forall (m : Message) (bom : Bag_of_message) (s1 s2 s3 s4 : Site), In_queue Message m (Collect_message Message bom s1 s2 s3 s4) -> In_queue Message m (bom s3 s4).