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diff --git a/matita/matita/contribs/lambda_delta/basic_2/reducibility/xpr_aaa.ma b/matita/matita/contribs/lambda_delta/basic_2/reducibility/xpr_aaa.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 "basic_2/static/ssta_aaa.ma".
+include "basic_2/reducibility/lcpr_aaa.ma".
+include "basic_2/reducibility/xpr.ma".
+
+(* EXTENDED PARALLEL REDUCTION ON TERMS *************************************)
+
+(* Properties on atomic arity assignment for terms **************************)
+
+lemma xpr_aaa: ∀h,g,L,T,A. L ⊢ T ⁝ A → ∀U. ⦃h, L⦄ ⊢ T ➸[g] U → L ⊢ U ⁝ A.
+#h #g #L #T #A #HT #U * [2: * ] /2 width=3/ /2 width=6/
+qed.