--- /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/reducibility/lfpr.ma".
+include "basic_2/reducibility/cfpr_cpr.ma".
+
+(* FOCALIZED PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ***********************)
+
+(* Properties on context-free parallel reduction for closures ***************)
+
+lemma fpr_lfpr: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ➡ ⦃L2, T2⦄ → ⦃L1⦄ ➡ ⦃L2⦄.
+#L1 #L2 #T1 #T2 #H
+elim (fpr_inv_all … H) -H /2 width=3/
+qed.
+
+(* Inversion lemmas on context-free parallel reduction for closures *********)
+
+lemma lfpr_inv_fpr: ∀L1,L2. ⦃L1⦄ ➡ ⦃L2⦄ → ∀T. ⦃L1, T⦄ ➡ ⦃L2, T⦄.
+#L1 #L2 * /2 width=4/
+qed-.