--- /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/ltpr.ma".
+include "basic_2/equivalence/lcpcs.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON LOCAL ENVIRONMENTS *************)
+
+(* Properties on context-free parallel reduction for local environments *****)
+
+lemma ltpr_lcpcs: ∀L1,L2. L1 ➡ L2 → L1 ⊢ ⬌* L2.
+#L1 #L2 #H elim H -L1 -L2 // /4 width=1/
+qed.