+(**************************************************************************)
+(* ___ *)
+(* ||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/dynamic/lsubv_cnv.ma".
+
+(* LOCAL ENVIRONMENT REFINEMENT FOR NATIVE VALIDITY *************************)
+
+(* Main properties **********************************************************)
+
+(* Note: not valid in Basic_2A1 *)
+theorem lsubv_trans (a) (h) (G): Transitive … (lsubv a h G).
+#a #h #G #L1 #L #H elim H -L1 -L //
+[ #I #K1 #K #HK1 #IH #Y #H
+ elim (lsubv_inv_bind_sn … H) -H *
+ [ #K2 #HK2 #H destruct /3 width=1 by lsubv_bind/
+ | #K2 #W #V #HWV #HK2 #H1 #H2 destruct /3 width=3 by lsubv_cnv_trans, lsubv_beta/
+ ]
+| #K1 #K #W #V #HWV #_ #IH #Y #H
+ elim (lsubv_inv_abst_sn … H) -H
+ #K2 #HK2 #H1 destruct /3 width=1 by lsubv_beta/
+]
+qed-.