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diff --git a/matita/matita/contribs/lambdadelta/ground_2/xoa/ex_4_1_props.ma b/matita/matita/contribs/lambdadelta/ground_2/xoa/ex_4_1_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 "ground_2/xoa/xoa.ma".
+
+(* Properties with multiple existental quantifier (5, 1) ********************)
+
+lemma ex4_commute (A0) (P0,P1,P2,P3:A0→Prop):
+                  (∃∃x0. P0 x0 & P1 x0 & P2 x0 & P3 x0) → ∃∃x0. P2 x0 & P3 x0 & P0 x0 & P1 x0.
+#A0 #P0 #P1 #P2 #P3 * /2 width=5 by ex4_intro/
+qed-.