Remark del_trans_parent :
 forall s1 s2 : Site, parent (delete_trans c0 s0) s2 s1 -> parent c0 s2 s1.

(* Specifications: *)
Lemma del_trans_parent_cr : forall s3 s4 : Site, (parent c0 s3 s4 -> dt c0 s3 < dt c0 s4) -> parent (delete_trans c0 s0) s3 s4 -> dt (delete_trans c0 s0) s3 < dt (delete_trans c0 s0) s4.