End REC_INC_CTRL.
Section REC_INC_XY.
Variable c0 : Config.
Variable s1 s2 : Site.
Hypothesis
first_mess : first Message (bm c0 s1 owner) = value Message (inc_dec s2).
Hypothesis not_owner : s2 <> owner.
Remark rinc_trans_xi :
forall s0 : Site, xi (rec_inc_trans c0 s1 s2) s0 = xi c0 s0.
Remark rinc_trans_yi :
forall s0 : Site,
yi (rec_inc_trans c0 s1 s2) s0 =
(if eq_site_dec s0 s1 then (yi c0 s0 - 1)%Z else yi c0 s0).

Lemma rinc_trans_sigma_xi : sigma_xi (rec_inc_trans c0 s1 s2) = sigma_xi c0.