--- /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/static/lfxs_lfxs.ma".
+include "basic_2/static/lfeq.ma".
+
+(* SYNTACTIC EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES *********)
+
+(* Advanced forward lemmas **************************************************)
+
+(* Note: the proof should may invoke lfeq_transitive_inv_lfxs *)
+lemma lfeq_lfxs_trans: ∀R. c_reflexive … R → lfeq_transitive R →
+ ∀L1,L,T. L1 ≡[T] L →
+ ∀L2. L ⪤*[R, T] L2 → L1 ⪤*[R, T] L2.
+/3 width=9 by lfxs_trans_gen/ qed-.