Section REC_COP3_CTRL.
(* decompte de messages *)
Variable c0 : Config.
Variable s0 s1 s2 : Site.
Hypothesis not_owner : s1 <> owner.
Hypothesis first_mess : first Message (bm c0 s1 s2) = value Message copy.
Remark rcop3_trans_sigma_copy :
sigma_ctrl_copy s0 (bm (rec_copy3_trans c0 s1 s2)) =
(if eq_site_dec s0 s1
then  (sigma_ctrl_copy s0 (bm c0) - 1)%Z
else  sigma_ctrl_copy s0 (bm c0)).
Remark rcop3_trans_sigma_dec :
sigma_ctrl_dec s0 (bm (rec_copy3_trans c0 s1 s2)) =
sigma_ctrl_dec s0 (bm c0).
Remark rcop3_trans_sigma_inc :
sigma_ctrl_inc s0 (bm (rec_copy3_trans c0 s1 s2)) =
(if eq_site_dec s0 s1
then  (sigma_ctrl_inc s0 (bm c0) + 1)%Z
else  sigma_ctrl_inc s0 (bm c0)).

Lemma rcop3_trans_sigma_ctrl :
sigma_ctrl s0 (bm (rec_copy3_trans c0 s1 s2)) = sigma_ctrl s0 (bm c0).