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diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/scpes/scpes.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/scpes/scpes.etc
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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/scpds.ma".
+
+(* STRATIFIED DECOMPOSED PARALLEL EQUIVALENCE FOR TERMS *********************)
+
+definition scpes: ∀h. sd h → nat → nat → relation4 genv lenv term term ≝
+                  λh,o,d1,d2,G,L,T1,T2.
+                  ∃∃T. ⦃G, L⦄ ⊢ T1 •*➡*[h, o, d1] T & ⦃G, L⦄ ⊢ T2 •*➡*[h, o, d2] T.
+
+interpretation "stratified decomposed parallel equivalence (term)"
+   'DPConvStar h o d1 d2 G L T1 T2 = (scpes h o d1 d2 G L T1 T2).
+
+(* Basic properties *********************************************************)
+
+lemma scpds_div: ∀h,o,G,L,T1,T2,T,d1,d2.
+                 ⦃G, L⦄ ⊢ T1 •*➡*[h, o, d1] T → ⦃G, L⦄ ⊢ T2 •*➡*[h, o, d2] T →
+                 ⦃G, L⦄ ⊢ T1 •*⬌*[h, o, d1, d2] T2.
+/2 width=3 by ex2_intro/ qed.
+
+lemma scpes_sym: ∀h,o,G,L,T1,T2,d1,d2. ⦃G, L⦄ ⊢ T1 •*⬌*[h, o, d1, d2] T2 →
+                 ⦃G, L⦄ ⊢ T2 •*⬌*[h, o, d2, d1] T1.
+#h #o #G #L #T1 #T2 #L1 #d2 * /2 width=3 by scpds_div/
+qed-.