(* This program is free software; you can redistribute it and/or      *)
(* modify it under the terms of the GNU Lesser General Public License *)
(* as published by the Free Software Foundation; either version 2.1   *)
(* of the License, or (at your option) any later version.             *)
(*                                                                    *)
(* This program is distributed in the hope that it will be useful,    *)
(* but WITHOUT ANY WARRANTY; without even the implied warranty of     *)
(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
(*                                                                    *)
(* You should have received a copy of the GNU Lesser General Public   *)
(* License along with this program; if not, write to the Free         *)
(* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA *)
(* 02110-1301 USA                                                     *)
Require Export DistributedReferenceCounting.machine4.machine.
Require Export DistributedReferenceCounting.machine4.cardinal.
Require Export DistributedReferenceCounting.machine4.comm.
Unset Standard Proposition Elimination Names.
(** Changes with machine1: - As receive table owner equals 1, initally, I should add -1 - Base cases had to be changed - inductive case, proof is unchanged *)
Section INVARIANT1.
Remark add_reduce1 :
forall x1 x2 y : Z, x1 = x2 -> (y + x1 - 1)%Z = (y + x2 - 1)%Z.

(* Specifications: *)
Lemma invariant1_init :
sigma_send_table send_init =
(sigma_receive_table rec_init + sigma_weight bag_init - 1)%Z.
Lemma invariant1_inductive :
forall (c : Config) (t : class_trans c),
legal c ->
sigma_send_table (st c) =
(sigma_receive_table (rt c) + sigma_weight (bm c) - 1)%Z ->
sigma_send_table (st (transition c t)) =
(sigma_receive_table (rt (transition c t)) +
sigma_weight (bm (transition c t)) - 1)%Z.
Lemma invariant1 :
forall c : Config,
legal c ->
sigma_send_table (st c) =
(sigma_receive_table (rt c) + sigma_weight (bm c) - 1)%Z.