--- /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/relocation/lex.ma".
+include "basic_2/static/lfxs_fqup.ma".
+
+(* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)
+
+(* Properties with generic extension of a context-sensitive relation ********)
+
+lemma lfxs_lex: ∀R,L1,L2. L1 ⪤[R] L2 → ∀T. L1 ⪤*[R, T] L2.
+#R #L1 #L2 * #f #Hf #HL12 #T
+elim (frees_total L1 T) #g #Hg
+/4 width=5 by lexs_sdj, sdj_isid_sn, ex2_intro/
+qed.