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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs_lpr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs_lpr.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/cpms_lpr.ma".
+include "basic_2/rt_computation/cprs_ctc.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL R-COMPUTATION FOR TERMS ***********************)
+
+(* Properties concerning sn parallel reduction on local environments ********)
+
+(* Basic_1: uses: pr3_pr2_pr2_t *)
+(* Basic_1: includes: pr3_pr0_pr2_t *)
+lemma lpr_cpr_trans (h) (G): s_r_transitive … (λL. cpm h G L 0) (λ_. lpr h G).
+/3 width=4 by cprs_inv_CTC, lpr_cpm_trans, ltc_inv_CTC/
+qed-.
+
+(* Basic_1: uses: pr3_pr2_pr3_t pr3_wcpr0_t *)
+lemma lpr_cprs_trans (h) (G): s_rs_transitive … (λL. cpm h G L 0) (λ_. lpr h G).
+#h #G @s_r_trans_CTC1 /2 width=3 by lpr_cpr_trans/ (**) (* full auto fails *)
+qed-.