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(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
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(* 02110-1301 USA                                                     *)
Require Export DistributedReferenceCounting.machine3.machine.
Require Export DistributedReferenceCounting.machine3.cardinal.
Require Export DistributedReferenceCounting.machine3.comm.
Unset Standard Proposition Elimination Names.
Section ALTERNATE.
Inductive alternate : queue Message -> Prop :=
| alt_null : alternate (empty Message)
| alt_single_inc :
forall s0 : Site,
alternate (input Message (inc_dec s0) (empty Message))
| alt_any_alt :
forall (qm : queue Message) (m : Message),
(forall s : Site, m <> inc_dec s) ->
alternate qm -> alternate (input Message m qm)
| alt_inc_dec :
forall (qm : queue Message) (s0 : Site),
alternate qm ->
alternate (input Message (inc_dec s0) (input Message dec qm)).

(* Specifications: *)
Lemma dec_is_not_inc : forall s : Site, dec <> inc_dec s.
Inductive D_queue : queue Message -> Prop :=
| D_empty : D_queue (empty Message)
| D_dec :
forall qm : queue Message,
alternate qm -> D_queue (input Message dec qm).
Lemma not_D_queue :
forall (q0 : queue Message) (m : Message),
m <> dec -> ~ D_queue (input Message m q0).
Lemma D_queue_is_alternate :
forall q0 : queue Message, D_queue q0 -> alternate q0.
Lemma alt_first_out :
forall q0 : queue Message, alternate q0 -> alternate (first_out Message q0).
Lemma D_first_out :
forall q0 : queue Message, D_queue q0 -> D_queue (first_out Message q0).