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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpre_csx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpre_csx.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_transition/cpm_cpx.ma".
+include "basic_2/rt_transition/cnr_tdeq.ma".
+include "basic_2/rt_computation/csx.ma".
+include "basic_2/rt_computation/cpre.ma".
+
+(* EVALUATION FOR CONTEXT-SENSITIVE PARALLEL R-TRANSITION ON TERMS **********)
+
+(* Properties with strong normalization for unbound rt-transition for terms *)
+
+(* Basic_1: was just: nf2_sn3 *)
+lemma cpre_total_csx (h) (G) (L):
+      ∀T1. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ → ∃T2. ⦃G,L⦄ ⊢ T1 ➡*[h] 𝐍⦃T2⦄.
+#h #G #L #T1 #H
+@(csx_ind … H) -T1 #T1 #_ #IHT1
+elim (cnr_dec_tdeq h G L T1) [ /3 width=3 by ex_intro, cpme_intro/ ] *
+#T0 #HT10 #HnT10
+elim (IHT1 … HnT10) -IHT1 -HnT10 [| /2 width=2 by cpm_fwd_cpx/ ]
+#T2 * /4 width=3 by cprs_step_sn, ex_intro, cpme_intro/
+qed-.