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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_lpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_lpxs.ma
index 3844f8620..48d1d0d1f 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_lpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_lpxs.ma
@@ -1,4 +1,27 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/rt_computation/cpms_cpxs.ma".
+include "basic_2/rt_computation/lpxs.ma".
 include "basic_2/rt_computation/lprs.ma".
 
-lemma lprs_lpxs: ∀h,g,G,L1,L2. ⦃G, L1⦄ ⊢ ➡* L2 → ⦃G, L1⦄ ⊢ ➡*[h, g] L2.
-/3 width=3 by lpr_lpx, monotonic_TC/ qed.
+(* PARALLEL R-COMPUTATION FOR FULL LOCAL ENVIRONMENTS ***********************)
+
+(* Forward lemmas with extended rt-computation for full local environments **)
+
+(* Basic_2A1: was: lprs_lpxs *)
+(* Note: original proof uses lpr_fwd_lpx and monotonic_TC *)
+lemma lprs_fwd_lpxs (h) (G):
+      ∀L1,L2. ❪G,L1❫ ⊢ ➡*[h,0] L2 → ❪G,L1❫ ⊢ ⬈* L2.
+/3 width=3 by cpms_fwd_cpxs, lex_co/ qed-.