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 : st (rec_dec_trans c0 s1 s2) s0 = (if eq_site_dec s0 s2 then (st c0 s0 - 1)%Z else st c0 s0).