End DEL_ALT.
Section DEL_RELAT.
(* relation parent *)
Variable c0 : Config.
Variable s0 : Site.
Remark del_trans_parent :
forall s1 s2 : Site, parent (delete_trans c0 s0) s2 s1 -> parent c0 s2 s1.

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.