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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  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_theq_vector.ma".
  18 include "basic_2/rt_computation/csx_simple_theq.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,T. 𝐒⦃T⦄ → ⦃G, L⦄ ⊢ ⬈[h] 𝐍⦃T⦄ →
  27                      ∀Vs. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃Vs⦄ → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⒶVs.T⦄.
  28 #h #G #L #T #H1T #H2T #Vs elim Vs -Vs
  29 [ #_ normalize in ⊢ (????%); /2 width=1 by cnx_csx/
  30 | #V #Vs #IHV #H
  31   elim (csxv_inv_cons … H) -H #HV #HVs
  32   @csx_appl_simple_theq /2 width=1 by applv_simple/ -IHV -HV -HVs
  33   #X #H #H0
  34   lapply (cpxs_fwd_cnx_vector … H) -H // -H1T -H2T #H
  35   elim (H0) -H0 //
  36 ]
  37 qed.
  38
  39 (* Advanced properties ******************************************************)
  40
  41 lemma csx_applv_sort: ∀h,G,L,s,Vs. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃Vs⦄ → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⒶVs.⋆s⦄.
  42 /3 width=6 by csx_applv_cnx, cnx_sort, simple_atom/ qed.