matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cnx_vector.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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   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 (* STRONGLY NORMALIZING TERM VECTORS FOR UNBOUND PARALLEL RT-TRANSITION *****)
  16
  17 include "basic_2/rt_computation/cpxs_teqo_vector.ma".
  18 include "basic_2/rt_computation/csx_simple_teqo.ma".
  19 include "basic_2/rt_computation/csx_cnx.ma".
  20 include "basic_2/rt_computation/csx_cpxs.ma".
  21 include "basic_2/rt_computation/csx_vector.ma".
  22
  23 (* Properties with normal terms for unbound parallel rt-transition **********)
  24
  25 (* Basic_1: was just: sn3_appls_lref *)
  26 lemma csx_applv_cnx (h) (G) (L):
  27       ∀T. 𝐒❪T❫ → ❪G,L❫ ⊢ ⬈𝐍[h] T →
  28       ∀Vs. ❪G,L❫ ⊢ ⬈*𝐒[h] Vs → ❪G,L❫ ⊢ ⬈*𝐒[h] ⒶVs.T.
  29 #h #G #L #T #H1T #H2T #Vs elim Vs -Vs
  30 [ #_ normalize in ⊢ (????%); /2 width=1 by cnx_csx/
  31 | #V #Vs #IHV #H
  32   elim (csxv_inv_cons … H) -H #HV #HVs
  33   @csx_appl_simple_teqo /2 width=1 by applv_simple/ -IHV -HV -HVs
  34   #X #H #H0
  35   lapply (cpxs_fwd_cnx_vector … H) -H // -H1T -H2T #H
  36   elim (H0) -H0 //
  37 ]
  38 qed.
  39
  40 (* Advanced properties ******************************************************)
  41
  42 (* Note: strong normalization does not depend on this any more *)
  43 lemma csx_applv_sort (h) (G) (L):
  44       ∀s,Vs. ❪G,L❫ ⊢ ⬈*𝐒[h] Vs → ❪G,L❫ ⊢ ⬈*𝐒[h] ⒶVs.⋆s.
  45 /3 width=6 by csx_applv_cnx, cnx_sort, simple_atom/ qed.