--- /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 "apps_2/models/model_li.ma".
+include "apps_2/models/veq_vdrop.ma".
+
+(* EVALUATION EQUIVALENCE ***************************************************)
+
+(* Properties with local environment interpretation *************************)
+
+lemma li_repl_back (M) (gv): is_model M →
+ ∀L,lv1. lv1 ϵ ⟦L⟧[gv] →
+ ∀lv2. lv1 ≗{M} lv2 → lv2 ϵ ⟦L⟧[gv].
+#M #gv #HM #L #lv1 #H elim H -L -lv1 //
+[ #lv1 #d1 #K #V #_ #Hd #IH #y #H
+ elim (veq_inv_vlift_sn … H) -H #lv2 #d2 #Hlv12 #Hd12 #Hy
+ /5 width=5 by li_repl, li_abbr, ti_comp_l, mq/
+| #lv1 #d1 #K #W #_ #IH #y #H
+ elim (veq_inv_vlift_sn … H) -H #lv2 #d2 #Hlv12 #_ #Hy
+ /4 width=3 by li_repl, li_abst/
+| #lv1 #d1 #I #K #_ #IH #y #H
+ elim (veq_inv_vlift_sn … H) -H #lv2 #d2 #Hlv12 #_ #Hy
+ /4 width=3 by li_repl, li_unit/
+| #lv1 #lv #L #_ #Hlv1 #IH #lv2 #Hlv2
+ @IH /2 width=3 by exteq_veq_trans/
+]
+qed-.