Section INVARIANT1.
Remark add_reduce1 :
forall x1 x2 y : Z, x1 = x2 -> (y + x1 - 1)%Z = (y + x2 - 1)%Z.

Lemma invariant1_init :
sigma_send_table send_init =
(sigma_receive_table rec_init + sigma_weight bag_init - 1)%Z.