update in models and ground_2

[helm.git] / matita / matita / contribs / lambdadelta / apps_2 / models / veq_li.ma

diff --git a/matita/matita/contribs/lambdadelta/apps_2/models/veq_li.ma b/matita/matita/contribs/lambdadelta/apps_2/models/veq_li.ma
new file mode 100644 (file)
index 0000000..717a039
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/apps_2/models/veq_li.ma
@@ -0,0 +1,36 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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.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_push_sn … H) -H #lv2 #d2 #Hlv12 #Hd12 #H destruct
+  /4 width=5 by li_abbr, ti_comp_l, mr/
+| #lv1 #d1 #K #W #_ #IH #y #H
+  elim (veq_inv_push_sn … H) -H #lv2 #d2 #Hlv12 #_ #H destruct
+  /3 width=1 by li_abst/
+| #lv1 #d1 #I #K #_ #IH #y #H
+  elim (veq_inv_push_sn … H) -H #lv2 #d2 #Hlv12 #_ #H destruct
+  /3 width=1 by li_unit/
+]
+qed-.