--- /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/rt_computation/fpbs_lpxs.ma".
+include "basic_2/rt_computation/fpbg.ma".
+
+(* PROPER PARALLEL RST-COMPUTATION FOR CLOSURES *****************************)
+
+(* Properties with unbound rt-computation on full local environments ********)
+
+(* Basic_2A1: uses: lpxs_fpbg *)
+lemma lpxs_lfdneq_fpbg: ∀h,o,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈*[h] L2 →
+ (L1 ≛[h, o, T] L2 → ⊥) → ⦃G, L1, T⦄ >[h, o] ⦃G, L2, T⦄.
+#h #o #G #L1 #L2 #T #H #H0
+elim (lpxs_lfdneq_inv_step_sn … H … H0) -H -H0
+/4 width=7 by fpb_lpx, lpxs_ffdeq_fpbs, ffdeq_intro_sn, ex2_3_intro/
+qed.