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diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/lsubr/dxprs_lpss.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/lsubr/dxprs_lpss.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/unfold/sstas_lpss.ma".
-include "basic_2/computation/cprs_lpss.ma".
-include "basic_2/computation/dxprs.ma".
-
-(* DECOMPOSED EXTENDED PARALLEL COMPUTATION ON TERMS ************************)
-
-(* Properties about sn parallel substitution for local environments *********)
-
-lemma dxprs_lpss_conf: ∀h,g,L1,T,U1. ⦃h, L1⦄ ⊢ T •*➡*[g] U1 → ∀L2. L1 ⊢ ▶* L2 →
-                       ∃∃U2. ⦃h, L2⦄ ⊢ T •*➡*[g] U2 & L1 ⊢ U1 ▶* U2.
-#h #g #L1 #T #U1 * #U #HTU #HU1 #L2 #HL12
-elim (sstas_lpss_conf … HTU … HL12) -HTU #U0 #HTU0 #HU0
-elim (cprs_cpss_conf … HU1 … HU0) -U #U #HU1 #HU0
-elim (cprs_lpss_conf_sn … HU0 … HL12) -HU0 -HL12 #U2 #HU2 #HU02
-lapply (cpss_trans … HU1 … HU2) -U /3 width=3/
-qed-.
-
-lemma dxprs_cpss_conf: ∀h,g,L,T1,U1. ⦃h, L⦄ ⊢ T1 •*➡*[g] U1 → ∀T2. L ⊢ T1 ▶* T2 →
-                       ∃∃U2. ⦃h, L⦄ ⊢ T2 •*➡*[g] U2 & L ⊢ U1 ▶* U2.
-#h #g #L #T1 #U1 * #W1 #HTW1 #HWU1 #T2 #HT12
-elim (sstas_cpss_conf … HTW1 … HT12) -T1 #W2 #HTW2 #HW12
-elim (cprs_cpss_conf … HWU1 … HW12) -W1 /3 width=3/
-qed-.
-
-lemma dxprs_cpss_lpss_conf: ∀h,g,L1,T1,U1. ⦃h, L1⦄ ⊢ T1 •*➡*[g] U1 →
-                            ∀T2. L1 ⊢ T1 ▶* T2 → ∀L2. L1 ⊢ ▶* L2 →
-                            ∃∃U2. ⦃h, L2⦄ ⊢ T2 •*➡*[g] U2 & L1 ⊢ U1 ▶* U2.
-#h #g #L1 #T1 #U1 #HTU1 #T2 #HT12 #L2 #HL12
-elim (dxprs_cpss_conf … HTU1 … HT12) -T1 #U2 #HTU2 #HU12
-elim (dxprs_lpss_conf … HTU2 … HL12) -HTU2 -HL12 #U #HT2U #HU2
-lapply (cpss_trans … HU12 … HU2) -U2 /2 width=3/
-qed-.