matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubv_lsubv.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 "basic_2/dynamic/lsubv_cnv.ma".
  16
  17 (* LOCAL ENVIRONMENT REFINEMENT FOR NATIVE VALIDITY *************************)
  18
  19 (* Main properties **********************************************************)
  20
  21 (* Note: not valid in Basic_2A1 *)
  22 theorem lsubv_trans (a) (h) (G): Transitive … (lsubv a h G).
  23 #a #h #G #L1 #L #H elim H -L1 -L //
  24 [ #I #K1 #K #HK1 #IH #Y #H
  25   elim (lsubv_inv_bind_sn … H) -H *
  26   [ #K2 #HK2 #H destruct /3 width=1 by lsubv_bind/
  27   | #K2 #W #V #HWV #HK2 #H1 #H2 destruct /3 width=3 by lsubv_cnv_trans, lsubv_beta/
  28   ]
  29 | #K1 #K #W #V #HWV #_ #IH #Y #H
  30   elim (lsubv_inv_abst_sn … H) -H
  31   #K2 #HK2 #H1 destruct /3 width=1 by lsubv_beta/
  32 ]
  33 qed-.