matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpre_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_tdeq.ma".
  17 include "basic_2/rt_computation/csx.ma".
  18 include "basic_2/rt_computation/cpre.ma".
  19
  20 (* EVALUATION FOR CONTEXT-SENSITIVE PARALLEL R-TRANSITION ON TERMS **********)
  21
  22 (* Properties with strong normalization for unbound rt-transition for terms *)
  23
  24 (* Basic_1: was just: nf2_sn3 *)
  25 lemma csx_cpre (h) (G) (L):
  26       ∀T1. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ → ∃T2. ⦃G, L⦄ ⊢ T1 ➡*[h] 𝐍⦃T2⦄.
  27 #h #G #L #T1 #H
  28 @(csx_ind … H) -T1 #T1 #_ #IHT1
  29 elim (cnr_dec_tdeq h G L T1) [ /3 width=3 by ex_intro, conj/ ] *
  30 #T0 #HT10 #HnT10
  31 elim (IHT1 … HnT10) -IHT1 -HnT10 [| /2 width=2 by cpm_fwd_cpx/ ]
  32 #T2 * /4 width=3 by cprs_step_sn, ex_intro, conj/
  33 qed-.