proposition: Lemma rdec_trans_st : st (rec_dec_trans c0 s1 s2) s0 = (if eq_site_dec s0 s2 then (st c0 s0 - 1)%Z else st c0 s0).
proof: Proof. simpl in |- *; case (eq_site_dec s0 s2); intro. rewrite e; apply pred_dec_send_table. apply no_dec_send_table; auto. Qed.
imports: init table_act mess_act