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