matita/matita/contribs/lambdadelta/apps_2/models/veq_li.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "apps_2/models/model_li.ma".
  16 include "apps_2/models/veq.ma".
  17
  18 (* EVALUATION EQUIVALENCE  **************************************************)
  19
  20 (* Properties with local environment interpretation *************************)
  21
  22 lemma li_repl_back (M) (gv): is_model M →
  23                              ∀L,lv1. lv1 ϵ ⟦L⟧[gv] →
  24                              ∀lv2. lv1 ≗{M} lv2 → lv2 ϵ ⟦L⟧[gv].
  25 #M #gv #HM #L #lv1 #H elim H -L -lv1 //
  26 [ #lv1 #d1 #K #V #_ #Hd #IH #y #H
  27   elim (veq_inv_push_sn … H) -H #lv2 #d2 #Hlv12 #Hd12 #H destruct
  28   /4 width=5 by li_abbr, ti_comp_l, mr/
  29 | #lv1 #d1 #K #W #_ #IH #y #H
  30   elim (veq_inv_push_sn … H) -H #lv2 #d2 #Hlv12 #_ #H destruct
  31   /3 width=1 by li_abst/
  32 | #lv1 #d1 #I #K #_ #IH #y #H
  33   elim (veq_inv_push_sn … H) -H #lv2 #d2 #Hlv12 #_ #H destruct
  34   /3 width=1 by li_unit/
  35 ]
  36 qed-.