+(**************************************************************************)
+(* ___ *)
+(* ||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 "ground_2/lib/exteq.ma".
+include "apps_2/models/model_vpush.ma".
+include "apps_2/models/tm.ma".
+
+(* TERM MODEL ***************************************************************)
+
+(* Properties with push for model evaluation ********************************)
+
+lemma tm_vpush_vlift_join_O (h) (v) (T): ⇡[0]⫯{TM h}[0←T]v ≐ ⇡[0←↑[1]T]v.
+#h #v #T #i
+elim (eq_or_gt i) #Hi destruct
+[ >mf_vpush_eq >mf_vlift_rw >vpush_eq //
+| >mf_vpush_gt // >mf_vlift_rw >vpush_gt //
+]
+qed.