matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_fsb.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/cnv_fsb.ma".
  16 include "basic_2/dynamic/nta.ma".
  17
  18 (* NATIVE TYPE ASSIGNMENT FOR TERMS *****************************************)
  19
  20 (* Forward lemmas with strongly rst-normalizing closures ********************)
  21
  22 (* Note: this is an extended stong normalization property *)
  23 (* Note: this might use fsb_inv_cast (still to be proved) *)
  24 (* Basic_1: uses: ty3_sn3 *)
  25 (* Basic_2A1: uses: nta_fwd_csn *)
  26 theorem nta_fwd_fsb (h) (a) (G) (L):
  27         ∀T,U. ❪G,L❫ ⊢ T :[h,a] U →
  28         ∧∧ ≥𝐒[h] ❪G,L,T❫ & ≥𝐒[h] ❪G,L,U❫.
  29 #h #a #G #L #T #U #H
  30 elim (cnv_inv_cast … H) #X #HU #HT #_ #_ -X
  31 /3 width=2 by cnv_fwd_fsb, conj/
  32 qed-.