Definition rec_copy2_trans (c : Config) (s2 : Site) :=
  mkconfig (S (time c)) (dt c) (st c) (Set_rec_table (rt c) s2)
    (Collect_message (bm c) owner s2).

Lemma rcop2_trans_ctrl_copy : forall s1 : Site, ctrl_copy s0 s1 (bm (rec_copy2_trans c0 s2)) = (if eq_site_dec s0 owner then if eq_site_dec s1 s2 then (ctrl_copy s0 s1 (bm c0) - 1)%Z else ctrl_copy s0 s1 (bm c0) else ctrl_copy s0 s1 (bm c0)).