Section INVARIANT5.
(* In this file, we establish the following inequality Int + Sum copy + Sum dec - Sum inc_dec >= 0  *)
(* The message queue between a site and the owner has a particular structure.  Messages dec and inc_dec are alternated. *)

Lemma count_alt_queue :
forall q : queue Message,
alternate q ->
(reduce Message dec_count q + 1 >= reduce Message new_inc_count q)%Z /\
(D_queue q ->
(reduce Message dec_count q >= reduce Message new_inc_count q)%Z).