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.