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diff --git a/matita/matita/contribs/lambdadelta/basic_2A/computation/cpre.ma b/matita/matita/contribs/lambdadelta/basic_2A/computation/cpre.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_2A/notation/relations/predeval_4.ma".
+include "basic_2A/computation/cprs.ma".
+include "basic_2A/computation/csx.ma".
+
+(* EVALUATION FOR CONTEXT-SENSITIVE PARALLEL REDUCTION ON TERMS *************)
+
+definition cpre: relation4 genv lenv term term ≝
+                 λG,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 ∧ ⦃G, L⦄ ⊢ ➡ 𝐍⦃T2⦄.
+
+interpretation "evaluation for context-sensitive parallel reduction (term)"
+   'PRedEval G L T1 T2 = (cpre G L T1 T2).
+
+(* Basic properties *********************************************************)
+
+(* Basic_1: was just: nf2_sn3 *)
+lemma csx_cpre: ∀h,g,G,L,T1. ⦃G, L⦄ ⊢ ⬊*[h, g] T1 → ∃T2. ⦃G, L⦄ ⊢ T1 ➡* 𝐍⦃T2⦄.
+#h #g #G #L #T1 #H @(csx_ind … H) -T1
+#T1 #_ #IHT1 elim (cnr_dec G L T1) /3 width=3 by ex_intro, conj/
+* #T #H1T1 #H2T1 elim (IHT1 … H2T1) -IHT1 -H2T1 /2 width=2 by cpr_cpx/
+#T2 * /4 width=3 by cprs_strap2, ex_intro, conj/
+qed.