proposition: 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).
proof: Proof. intro; unfold yi in |- *. case (eq_site_dec s0 s1); intro. apply sigma__pred with (eq_E_dec := eq_site_dec) (x0 := s2). exact finite_site. rewrite rinc_trans_ctrl_inc. rewrite e; rewrite case_eq; apply case_eq. trivial. intros; rewrite rinc_trans_ctrl_inc. apply case_ineq; trivial. trivial. apply sigma_simpl; intros; rewrite rinc_trans_ctrl_inc. case (eq_site_dec x s2); intro. apply case_ineq; auto. trivial. trivial. Qed.
imports: init table_act mess_act