Definition copy_trans (c : Config) (s1 s2 : Site) :=
  mkconfig (S (time c)) (dt c) (Inc_send_table (st c) s1) 
    (rt c) (Post_message copy (bm c) s1 s2).

Lemma copy_trans_ctrl_copy : forall s' : Site, ctrl_copy s0 s' (bm (copy_trans c0 s1 s2)) = (if eq_site_dec s0 s1 then if eq_site_dec s' s2 then (ctrl_copy s0 s' (bm c0) + 1)%Z else ctrl_copy s0 s' (bm c0) else ctrl_copy s0 s' (bm c0)).