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diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/acle_acle.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/acle_acle.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 "static_2/syntax/acle.ma".
+
+(* APPLICABILITY CONDITION PREORDER *****************************************)
+
+(* Main properties **********************************************************)
+
+theorem acle_trans: Transitive … acle.
+#a1 #a #Ha1 #a2 #Ha2 #m1 #Hm1
+elim (Ha1 … Hm1) -Ha1 -Hm1 #m #Ha #Hm1
+elim (Ha2 … Ha) -Ha2 -Ha #m2 #Ha2 #Hm2
+/3 width=5 by transitive_le, ex2_intro/
+qed-.