--- /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 "static_2/static/rex_length.ma".
+include "static_2/i_static/rexs.ma".
+
+(* ITERATED EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ***)
+
+(* Forward lemmas with length for local environments ************************)
+
+(* Basic_2A1: uses: TC_lpx_sn_fwd_length *)
+lemma rexs_fwd_length: ∀R,L1,L2,T. L1 ⪤*[R, T] L2 → |L1| = |L2|.
+#R #L1 #L2 #T #H elim H -L2
+[ #L2 #HL12 >(rex_fwd_length … HL12) -HL12 //
+| #L #L2 #_ #HL2 #IHL1
+ >IHL1 -L1 >(rex_fwd_length … HL2) -HL2 //
+]
+qed-.