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(* 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.

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.