--- /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 "basic_2/static/ssta_aaa.ma".
+include "basic_2/reducibility/cpr_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 width=3/ /2 width=6/
+qed.