End DEL_EFFECT.
Section DEL_CTRL.
(* decompte de messages *)
Variable c0 : Config.
Variable s0 s1 : Site.

(* Specifications: *)
Lemma del_trans_ctrl_copy :
forall s2 : Site,
ctrl_copy s0 s2 (bm (delete_trans c0 s1)) = ctrl_copy s0 s2 (bm c0).
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)).
Lemma del_trans_ctrl_inc :
forall s2 : Site,
ctrl_inc s0 s2 (bm (delete_trans c0 s1)) = ctrl_inc s0 s2 (bm c0).