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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_lprs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_lprs.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/reduction/lpr_lpr.ma".
+include "basic_2/computation/lprs.ma".
+
+(* SN PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS ****************************)
+
+(* Advanced properties ******************************************************)
+
+lemma lprs_strip: ∀G. confluent2 … (lprs G) (lpr G).
+/3 width=3 by TC_strip1, lpr_conf/ qed-.
+
+(* Main properties **********************************************************)
+
+theorem lprs_conf: ∀G. confluent2 … (lprs G) (lprs G).
+/3 width=3 by TC_confluent2, lpr_conf/ qed-.
+
+theorem lprs_trans: ∀G. Transitive … (lprs G).
+/2 width=3 by trans_TC/ qed-.