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diff --git a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpes.ma b/matita/matita/contribs/lambdadelta/basic_2/equivalence/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/notation/relations/dpconvstar_8.ma".
-include "basic_2/computation/cpds.ma".
-
-(* DECOMPOSED EXTENDED PARALLEL EQUIVALENCE FOR TERMS ***********************)
-
-definition cpes: ∀h. sd h → nat → nat → relation4 genv lenv term term ≝
-                 λh,g,l1,l2,G,L,T1,T2.
-                 ∃∃T. ⦃G, L⦄ ⊢ T1 •*➡*[h, g, l1] T & ⦃G, L⦄ ⊢ T2 •*➡*[h, g, l2] T.
-
-interpretation "decomposed extended parallel equivalence (term)"
-   'DPConvStar h g l1 l2 G L T1 T2 = (cpes h g l1 l2 G L T1 T2).
-
-(* Basic properties *********************************************************)
-
-lemma cpds_div: ∀h,g,G,L,T1,T2,T,l1,l2.
-                ⦃G, L⦄ ⊢ T1 •*➡*[h, g, l1] T → ⦃G, L⦄ ⊢ T2 •*➡*[h, g, l2] T →
-                ⦃G, L⦄ ⊢ T1 •*⬌*[h, g, l1, l2] T2.
-/2 width=3 by ex2_intro/ qed.
-
-lemma cpes_refl_O_O: ∀h,g,G,L,T,l. ⦃G, L⦄ ⊢ T ▪[h, g] l →
-                     ⦃G, L⦄ ⊢ T •*⬌*[h, g, 0, 0] T.
-/3 width=3 by cpds_refl, cpds_div/ qed.
-
-lemma cpes_sym: ∀h,g,G,L,T1,T2,l1,l2. ⦃G, L⦄ ⊢ T1 •*⬌*[h, g, l1, l2] T2 →
-                ⦃G, L⦄ ⊢ T2 •*⬌*[h, g, l2, l1] T1.
-#h #g #G #L #T1 #T2 #L1 #l2 * /2 width=3 by cpds_div/
-qed-.