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).