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diff --git a/matita/contribs/RELATIONAL/NLE/props.ma b/matita/contribs/RELATIONAL/NLE/props.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+
+
+include "NLE/order.ma".
+
+theorem nle_trans_succ: \forall x,y. x <= y \to x <= succ y.
+ intros. elim H; clear H x y; autobatch.
+qed.
+
+theorem nle_gt_or_le: \forall x, y. y > x \lor y <= x.
+ intros 2; elim y; clear y;
+ [ autobatch
+ | decompose;
+   [ lapply linear nle_inv_succ_1 to H1
+   | lapply linear nle_lt_or_eq to H1
+   ]; decompose; destruct; autobatch depth = 4
+ ].
+qed.