End COPY_EFFECT.
Section COPY_CTRL.
(* decompte de messages *)
Variable c0 : Config.
Variable s0 s1 s2 : Site.

(* Specifications: *)
Lemma copy_trans_ctrl_copy :
forall s' : Site,
ctrl_copy s0 s' (bm (copy_trans c0 s1 s2)) =
(if eq_site_dec s0 s1
then
if eq_site_dec s' s2
then  (ctrl_copy s0 s' (bm c0) + 1)%Z
else  ctrl_copy s0 s' (bm c0)
else  ctrl_copy s0 s' (bm c0)).
Lemma copy_trans_ctrl_dec :
forall s' : Site,
ctrl_dec s0 s' (bm (copy_trans c0 s1 s2)) = ctrl_dec s0 s' (bm c0).
Lemma copy_trans_ctrl_inc :
forall s' : Site,
ctrl_inc s0 s' (bm (copy_trans c0 s1 s2)) = ctrl_inc s0 s' (bm c0).