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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpes_cpes.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpes_cpes.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/lprs_cpms.ma".
+include "basic_2/rt_equivalence/cpes_cpms.ma".
+
+(* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-EQUIVALENCE FOR TERMS **************)
+
+(* Advanced forward lemmas **************************************************)
+
+lemma cpes_fwd_abst_bi (h) (n1) (n2) (p1) (p2) (G) (L):
+      ∀W1,W2,T1,T2. ⦃G,L⦄ ⊢ ⓛ{p1}W1.T1 ⬌*[h,n1,n2] ⓛ{p2}W2.T2 →
+      ∧∧ p1 = p2 & ⦃G,L⦄ ⊢ W1 ⬌*[h,0,O] W2.
+#h #n1 #n2 #p1 #p2 #G #L #W1 #W2 #T1 #T2 * #X #H1 #H2
+elim (cpms_inv_abst_sn … H1) #W0 #X0 #HW10 #_ #H destruct
+elim (cpms_inv_abst_bi … H2) #H #HW20 #_ destruct
+/3 width=3 by cpms_div, conj/
+qed-.
+
+(* Main properties **********************************************************)
+
+theorem cpes_cpes_trans (h) (n1) (n2) (G) (L) (T):
+        ∀T1. ⦃G,L⦄ ⊢ T ⬌*[h,n1,0] T1 →
+        ∀T2. ⦃G,L⦄ ⊢ T1 ⬌*[h,0,n2] T2 → ⦃G,L⦄ ⊢ T ⬌*[h,n1,n2] T2.
+#h #n1 #n2 #G #L #T #T1 #HT1 #T2 * #X #HX1 #HX2
+lapply (cpes_cprs_trans … HT1 … HX1) -T1 #HTX
+lapply (cpes_cpms_div … HTX … HX2) -X //
+qed-.