Definition rec_copy1_trans (c : Config) (s1 s2 : Site) :=
  mkconfig (S (time c)) (dt c) (st c) (rt c)
    (Post_message dec (Collect_message (bm c) s1 s2) s2 s1).

Lemma rcop1_trans_ctrl_dec : forall s3 : Site, ctrl_dec s0 s3 (bm (rec_copy1_trans c0 s1 s2)) = (if eq_site_dec s0 s1 then if eq_site_dec s3 s2 then (ctrl_dec s0 s3 (bm c0) + 1)%Z else ctrl_dec s0 s3 (bm c0) else ctrl_dec s0 s3 (bm c0)).