Definition delete_trans (c : Config) (s : Site) :=
  mkconfig (S (time c)) (dt c) (st c) (Reset_rec_table (rt c) s)
    (Post_message dec (bm c) s owner).

Lemma del_trans_ctrl_dec : forall s2 : Site, ctrl_dec s0 s2 (bm (delete_trans c0 s1)) = (if eq_site_dec owner s0 then if eq_site_dec s2 s1 then (ctrl_dec s0 s2 (bm c0) + 1)%Z else ctrl_dec s0 s2 (bm c0) else ctrl_dec s0 s2 (bm c0)).