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(* as published by the Free Software Foundation; either version 2.1   *)
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(*                                                                    *)
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(* GNU General Public License for more details.                       *)
(*                                                                    *)
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(* 02110-1301 USA                                                     *)
Require Export DistributedReferenceCounting.machine4.alternate.
Require Export DistributedReferenceCounting.machine4.invariant0.
Require Export DistributedReferenceCounting.machine4.invariant1.
Require Export DistributedReferenceCounting.machine4.invariant2.
Require Export DistributedReferenceCounting.machine4.invariant3.
Require Export DistributedReferenceCounting.machine4.invariant4.
Unset Standard Proposition Elimination Names.
(* Changes - proof of  1  for false_rt_D_queue. - proof of  1  for  legal_alternate. - owner_st_positive and its proof. *)
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).