--- /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/rdeq_fqup.ma".
+include "basic_2/rt_computation/rsx.ma".
+
+(* STRONGLY NORMALIZING REFERRED LOCAL ENV.S FOR UNBOUND RT-TRANSITION ******)
+
+(* Advanced properties ******************************************************)
+
+(* Basic_2A1: uses: lsx_atom *)
+lemma lfsx_atom (h) (G) (T): G ā¢ ā¬*[h,T] šā¦āā¦.
+#h #G #T
+@rsx_intro #Y #H #HnT
+lapply (lpx_inv_atom_sn ā¦ H) -H #H destruct
+elim HnT -HnT //
+qed.
+
+(* Advanced forward lemmas **************************************************)
+
+(* Basic_2A1: uses: lsx_fwd_bind_dx *)
+(* Note: the exclusion binder (ā§) makes this more elegant and much simpler *)
+(* Note: the old proof without the exclusion binder requires lreq *)
+lemma rsx_fwd_bind_dx_void (h) (G):
+ āp,I,L,V,T. G ā¢ ā¬*[h,ā{p,I}V.T] šā¦Lā¦ ā G ā¢ ā¬*[h,T] šā¦L.ā§ā¦.
+#h #G #p #I #L #V #T #H
+@(rsx_ind ā¦ H) -L #L1 #_ #IH
+@rsx_intro #Y #H #HT
+elim (lpx_inv_unit_sn ā¦ H) -H #L2 #HL12 #H destruct
+/4 width=4 by rdeq_fwd_bind_dx_void/
+qed-.
+
+(* Advanced inversion lemmas ************************************************)
+
+(* Basic_2A1: uses: lsx_inv_bind *)
+lemma rsx_inv_bind_void (h) (G):
+ āp,I,L,V,T. G ā¢ ā¬*[h,ā{p,I}V.T] šā¦Lā¦ ā
+ ā§ā§ G ā¢ ā¬*[h,V] šā¦Lā¦ & G ā¢ ā¬*[h,T] šā¦L.ā§ā¦.
+/3 width=4 by rsx_fwd_pair_sn, rsx_fwd_bind_dx_void, conj/ qed-.