+(**************************************************************************)
+(* ___ *)
+(* ||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_cpr.ma".
+include "basic_2/computation/cprs.ma".
+include "basic_2/computation/lfprs.ma".
+
+(* FOCALIZED PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS *********************)
+
+(* Advanced properties ******************************************************)
+
+lemma lfprs_pair_dx: ∀I,L1,L2. ⦃L1⦄ ➡ ⦃L2⦄ → ∀V1,V2. L2 ⊢ V1 ➡* V2 →
+ ⦃L1. ⓑ{I} V1⦄ ➡* ⦃L2. ⓑ{I} V2⦄.
+#I #L1 #L2 #HL12 #V1 #V2 #H @(cprs_ind … H) -V2
+/3 width=1/ /3 width=5/
+qed.