End DEL_CTRL.
Section DEL_XY.
Variable c0 : Config.
Variable s1 : Site.
Hypothesis rt_true : rt c0 s1 = true.
Remark del_trans_xi : forall s0 : Site, xi (delete_trans c0 s1) s0 = xi c0 s0.
Remark del_trans_yi : forall s0 : Site, yi (delete_trans c0 s1) s0 = yi c0 s0.

Lemma del_trans_sigma_xi : sigma_xi (delete_trans c0 s1) = sigma_xi c0.