matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprre_csx.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/rt_transition/cpm_cpx.ma".
  16 include "basic_2/rt_transition/cnr_teqx.ma".
  17 include "basic_2/rt_computation/csx.ma".
  18 include "basic_2/rt_computation/cprre.ma".
  19
  20 (* EVALUATION FOR CONTEXT-SENSITIVE PARALLEL R-TRANSITION ON TERMS **********)
  21
  22 (* Properties with strongly normalizing terms for extended rt-transition ****)
  23
  24 (* Basic_1: was just: nf2_sn3 *)
  25 (* Basic_2A1: was: csx_cpre *)
  26 lemma cprre_total_csx (h) (G) (L):
  27       ∀T1. ❪G,L❫ ⊢ ⬈*𝐒 T1 → ∃T2. ❪G,L❫ ⊢ T1 ➡*𝐍[h,0] T2.
  28 #h #G #L #T1 #H
  29 @(csx_ind … H) -T1 #T1 #_ #IHT1
  30 elim (cnr_dec_teqx h G L T1) [ /3 width=3 by ex_intro, cpmre_intro/ ] *
  31 #T0 #HT10 #HnT10
  32 elim (IHT1 … HnT10) -IHT1 -HnT10 [| /2 width=3 by cpm_fwd_cpx/ ]
  33 #T2 * /4 width=3 by cprs_step_sn, ex_intro, cpmre_intro/
  34 qed-.