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_st_rt : forall s1 : Site, st c0 s1 = 0%Z -> rt c0 s1 = true -> ((st c0 s0 > 0)%Z -> rt c0 s0 = true) -> (st (delete_trans c0 s1) s0 > 0)%Z -> rt (delete_trans c0 s1) s0 = true.