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_st_rt : ((st c0 s0 > 0)%Z -> rt c0 s0 = true) -> (st (rec_dec_trans c0 s1 s2) s0 > 0)%Z -> rt (rec_dec_trans c0 s1 s2) s0 = true.