End REC_COP2_EFFECT.
Section REC_COP2_CTRL.
(* decompte de messages *)
Variable c0 : Config.
Variable s0 s2 : Site.
Hypothesis first_mess : first Message (bm c0 owner s2) = value Message copy.

(* Specifications: *)
Lemma rcop2_trans_ctrl_copy :
forall s1 : Site,
ctrl_copy s0 s1 (bm (rec_copy2_trans c0 s2)) =
(if eq_site_dec s0 owner
then
if eq_site_dec s1 s2
then  (ctrl_copy s0 s1 (bm c0) - 1)%Z
else  ctrl_copy s0 s1 (bm c0)
else  ctrl_copy s0 s1 (bm c0)).
Lemma rcop2_trans_ctrl_dec :
forall s1 : Site,
ctrl_dec s0 s1 (bm (rec_copy2_trans c0 s2)) = ctrl_dec s0 s1 (bm c0).
Lemma rcop2_trans_ctrl_inc :
forall s1 : Site,
ctrl_inc s0 s1 (bm (rec_copy2_trans c0 s2)) = ctrl_inc s0 s1 (bm c0).