--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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-.