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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpes_cpms.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpes_cpms.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/cprs_cprs.ma".
+include "basic_2/rt_equivalence/cpes.ma".
+
+(* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-EQUIVALENCE FOR TERMS **************)
+
+(* Properties with t-bound rt-computation on terms **************************)
+
+lemma cpes_cprs_trans (h) (n) (G) (L) (T0):
+      ∀T1.  ⦃G,L⦄ ⊢ T1 ⬌*[h,n,0] T0 →
+      ∀T2.  ⦃G,L⦄ ⊢ T0 ➡*[h] T2 → ⦃G,L⦄ ⊢ T1 ⬌*[h,n,0] T2.
+#h #n #G #L #T0 #T1 * #T #HT1 #HT0 #T2 #HT02
+elim (cprs_conf … HT0 … HT02) -T0 #T0 #HT0 #HT20
+/3 width=3 by cpms_div, cpms_cprs_trans/
+qed-.
+
+lemma cpes_cpms_div (h) (n) (n1) (n2) (G) (L) (T0):
+      ∀T1.  ⦃G,L⦄ ⊢ T1 ⬌*[h,n,n1] T0 →
+      ∀T2.  ⦃G,L⦄ ⊢ T2 ➡*[n2,h] T0 → ⦃G,L⦄ ⊢ T1 ⬌*[h,n,n2+n1] T2.
+#h #n #n1 #n2 #G #L #T0 #T1 * #T #HT1 #HT0 #T2 #HT20
+lapply (cpms_trans … HT20 … HT0) -T0 #HT2
+/2 width=3 by cpms_div/
+qed-.