proposition: Lemma lt_sigma_xi_yi : (sigma_xi c0 > sigma_yi c0)%Z.
proof: Proof. apply Zlt_gt; unfold sigma_xi, sigma_yi in |- *; apply lt_sigma_sigma. intro; apply Zge_le; apply le_xi_yi; trivial. exists (root_parent s0); split. apply Zgt_lt; apply lt_root_xi_yi. apply in_s_LS. Qed.
imports: copy del rece_copy1 rece_copy2 rece_copy3 rece_dec rece_inc