--- /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/computation/csx_llpx.ma".
+include "basic_2/computation/llpxs.ma".
+
+(* CONTEXT-SENSITIVE EXTENDED STRONGLY NORMALIZING TERMS ********************)
+
+(* Properties on lazy sn extended computation for local environments ********)
+
+lemma csx_llpxs_conf: ∀h,g,G,L1,T. ⦃G, L1⦄ ⊢ ⬊*[h, g] T →
+ ∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g, T, 0] L2 → ⦃G, L2⦄ ⊢ ⬊*[h, g] T.
+#h #g #G #L1 #T #HT #L2 #H @(llpxs_ind … H) -L2 /3 by llpxs_strap1, csx_llpx_conf/
+qed-.