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- parallel reduction for local environments: we proved the equivalence
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diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/lcprs_cprs.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/lcprs_cprs.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/lcpr_cpr.ma".
-include "basic_2/computation/cprs.ma".
-include "basic_2/computation/lcprs.ma".
-
-(* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS *************)
-
-(* Advanced properties ******************************************************)
-
-lemma lcprs_pair_dx: ∀I,L1,L2. L1 ⊢ ➡ L2 → ∀V1,V2. L2 ⊢ V1 ➡* V2 →
-                     L1. ⓑ{I} V1 ⊢ ➡* L2. ⓑ{I} V2.
-#I #L1 #L2 #HL12 #V1 #V2 #H @(cprs_ind … H) -V2
-/3 width=1/ /3 width=5/
-qed.