--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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/xoa/ex_4_1.ma".
+
+(* Properties with multiple existental quantifier (4, 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-.