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_ctrl_dec : forall s0 s3 : Site, ctrl_dec s0 s3 (bm (rec_inc_trans c0 s1 s2)) = (if eq_site_dec s0 s2 then if eq_site_dec s3 owner then (ctrl_dec s0 s3 (bm c0) + 1)%Z else ctrl_dec s0 s3 (bm c0) else ctrl_dec s0 s3 (bm c0)).