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diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/lfprs_lfprs.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/lfprs_lfprs.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/reducibility/lfpr_lfpr.ma".
+include "basic_2/computation/lfprs_cprs.ma".
+
+(* FOCALIZED PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS *********************)
+
+(* Advanced properties ******************************************************)
+
+lemma lfprs_strip: ∀L,L1. ⦃L⦄ ➡* ⦃L1⦄ → ∀L2. ⦃L⦄ ➡ ⦃L2⦄ →
+                   ∃∃L0. ⦃L1⦄ ➡ ⦃L0⦄ & ⦃L2⦄ ➡* ⦃L0⦄.
+/3 width=3/ qed.
+
+(* Main properties **********************************************************)
+
+theorem lfprs_conf: ∀L,L1. ⦃L⦄ ➡* ⦃L1⦄ → ∀L2. ⦃L⦄ ➡* ⦃L2⦄ →
+                    ∃∃L0. ⦃L1⦄ ➡* ⦃L0⦄ & ⦃L2⦄ ➡* ⦃L0⦄.
+/3 width=3/ qed.
+
+theorem lfprs_trans: ∀L1,L. ⦃L1⦄ ➡* ⦃L⦄ → ∀L2. ⦃L⦄ ➡* ⦃L2⦄ → ⦃L1⦄ ➡* ⦃L2⦄.
+/2 width=3/ qed.
+
+lemma lfprs_pair: ∀L1,L2. ⦃L1⦄ ➡* ⦃L2⦄ → ∀V1,V2. L2 ⊢ V1 ➡* V2 →
+                  ∀I. ⦃L1. ⓑ{I} V1⦄ ➡* ⦃L2. ⓑ{I} V2⦄.
+#L1 #L2 #H @(lfprs_ind … H) -L2 /2 width=1/
+#L #L2 #_ #HL2 #IHL1 #V1 #V2 #HV12 #I
+@(lfprs_trans … (L.ⓑ{I}V1)) /2 width=1/
+qed.