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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_rdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_rdeq.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/cpxs_rdeq.ma".
+include "basic_2/rt_computation/cpms_cpxs.ma".
+
+(* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
+
+(* Properties with degree-based equivalence for local environments **********)
+
+lemma cpms_rdeq_conf_sn (h) (n) (o) (G) (L1) (L2):
+                        ∀T1,T2. ⦃G, L1⦄ ⊢ T1 ➡*[n,h] T2 →
+                        L1 ≛[h,o,T1] L2 → L1 ≛[h,o,T2] L2.
+/3 width=4 by cpms_fwd_cpxs, cpxs_rdeq_conf_sn/ qed-.
+
+lemma cpms_rdeq_conf_dx (h) (n) (o) (G) (L1) (L2):
+                        ∀T1,T2. ⦃G, L2⦄ ⊢ T1 ➡*[n,h] T2 →
+                        L1 ≛[h,o,T1] L2 → L1 ≛[h,o,T2] L2.
+/3 width=4 by cpms_fwd_cpxs, cpxs_rdeq_conf_dx/ qed-.