Definition rec_dec_trans (c : Config) (s1 s2 : Site) :=
  mkconfig (S (time c)) (dt c) (Dec_send_table (st c) s2) 
    (rt c) (Collect_message (bm c) s1 s2).

Lemma rdec_trans_ctrl_inc : forall s3 : Site, ctrl_inc s0 s3 (bm (rec_dec_trans c0 s1 s2)) = ctrl_inc s0 s3 (bm c0).