End REC_COP3_CTRL.
Section REC_COP3_XY.
Variable c0 : Config.
Variable s1 s2 : Site.
Hypothesis rt_true : rt c0 s2 = false.
Hypothesis not_owner : s1 <> owner.
Hypothesis first_mess : first Message (bm c0 s1 s2) = value Message copy.
Remark rcop3_trans_xi :
forall s0 : Site,
xi (rec_copy3_trans c0 s1 s2) s0 =
(if eq_site_dec s0 s2 then  (xi c0 s0 + 1)%Z else  xi c0 s0).
Remark rcop3_trans_yi :
forall s0 : Site,
yi (rec_copy3_trans c0 s1 s2) s0 =
(if eq_site_dec s0 s2 then  (yi c0 s0 + 1)%Z else yi c0 s0).

Lemma rcop3_trans_sigma_xi :
sigma_xi (rec_copy3_trans c0 s1 s2) = (sigma_xi c0 + 1)%Z.