Definition rec_copy3_trans (c : Config) (s1 s2 : Site) :=
  mkconfig (S (time c)) (Update_table (dt c) s2 (S (time c))) 
    (st c) (Set_rec_table (rt c) s2)
    (Post_message (inc_dec s1) (Collect_message (bm c) s1 s2) s2 owner).

Lemma rcop3_trans_ctrl_copy : forall s3 : Site, ctrl_copy s0 s3 (bm (rec_copy3_trans c0 s1 s2)) = (if eq_site_dec s0 s1 then if eq_site_dec s3 s2 then (ctrl_copy s0 s3 (bm c0) - 1)%Z else ctrl_copy s0 s3 (bm c0) else ctrl_copy s0 s3 (bm c0)).