End COPY_CTRL.
Section COPY_XY.
Variable c0 : Config.
Variable s1 s2 : Site.
Remark copy_trans_xi :
forall s0 : Site,
xi (copy_trans c0 s1 s2) s0 =
(if eq_site_dec owner s1
then
if eq_site_dec s0 s2 then  (xi c0 s0 + 1)%Z else  xi c0 s0
else  xi c0 s0).
Remark copy_trans_yi :
forall s0 : Site, yi (copy_trans c0 s1 s2) s0 = yi c0 s0.

Lemma copy_trans_sigma_xi :
sigma_xi (copy_trans c0 s1 s2) =
(if eq_site_dec owner s1
then  (sigma_xi c0 + 1)%Z
else  sigma_xi c0).