matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubv_cnv.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_cpms.ma".
  16
  17 (* LOCAL ENVIRONMENT REFINEMENT FOR NATIVE VALIDITY *************************)
  18
  19 (* Forward lemmas with native validity **************************************)
  20
  21 (* Basic_2A1: uses: lsubsv_snv_trans *)
  22 lemma lsubv_cnv_trans (a) (h) (G):
  23                       ∀L2,T. ⦃G,L2⦄ ⊢ T ![a,h] →
  24                       ∀L1. G ⊢ L1 ⫃![a,h] L2 → ⦃G,L1⦄ ⊢ T ![a,h].
  25 #a #h #G #L2 #T #H elim H -G -L2 -T //
  26 [ #I #G #K2 #V #HV #IH #L1 #H
  27   elim (lsubv_inv_bind_dx … H) -H * /3 width=1 by cnv_zero/
  28 | #I #G #K2 #i #_ #IH #L1 #H
  29   elim (lsubv_inv_bind_dx … H) -H * /3 width=1 by cnv_lref/
  30 | #p #I #G #L2 #V #T #_ #_ #IHV #IHT #L1 #HL12
  31   /4 width=1 by cnv_bind, lsubv_bind/
  32 | #n #p #G #L2 #V #W #T #U #Ha #_ #_ #HVW #HTU #IHV #IHT #L1 #HL
  33   /4 width=10 by lsubv_cpms_trans, cnv_appl/
  34 | #G #L2 #U #T #U0 #_ #_ #HU0 #HTU0 #IHU #IHT #L1 #HL12
  35   /4 width=6 by lsubv_cpms_trans, cnv_cast/
  36 ]
  37 qed-.