Definition rec_inc_trans (c : Config) (s1 s3 : Site) :=
  mkconfig (S (time c)) (dt c) (Inc_send_table (st c) owner) 
    (rt c) (Post_message dec (Collect_message (bm c) s1 owner) owner s3).

Lemma rinc_trans_st_rt : forall s0 : Site, s0 <> owner -> ((st c0 s0 > 0)%Z -> rt c0 s0 = true) -> (st (rec_inc_trans c0 s1 s2) s0 > 0)%Z -> rt (rec_inc_trans c0 s1 s2) s0 = true.