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diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs_drop.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs_drop.ma
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index 000000000..1b760d856
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+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs_drop.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/reduction/lpx_drop.ma".
+include "basic_2/computation/lpxs.ma".
+
+(* SN EXTENDED PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS *******************)
+
+(* Properies on local environment slicing ***********************************)
+
+lemma lpxs_drop_conf: ∀h,g,G. dropable_sn (lpxs h g G).
+/3 width=3 by dropable_sn_TC, lpx_drop_conf/ qed-.
+
+lemma drop_lpxs_trans: ∀h,g,G. dedropable_sn (lpxs h g G).
+/3 width=3 by dedropable_sn_TC, drop_lpx_trans/ qed-.
+
+lemma lpxs_drop_trans_O1: ∀h,g,G. dropable_dx (lpxs h g G).
+/3 width=3 by dropable_dx_TC, lpx_drop_trans_O1/ qed-.