matita/matita/contribs/lambdadelta/basic_2/etc/cpue/cpue_csx.etc

   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                  *)
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  13 (**************************************************************************)
  14
  15 include "basic_2/rt_transition/cpm_cpx.ma".
  16 include "basic_2/rt_transition/cnu_tdeq.ma".
  17 include "basic_2/rt_computation/csx.ma".
  18 include "basic_2/rt_computation/cpue.ma".
  19
  20 (* EVALUATION FOR T-UNBOUND RT-TRANSITION ON TERMS **************************)
  21
  22 (* Properties with strong normalization for unbound rt-transition for terms *)
  23
  24 lemma cpue_total_csx (h) (G) (L):
  25       ∀T1. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ → ∃T2. ⦃G,L⦄ ⊢ T1 ⥲*[h] 𝐍⦃T2⦄.
  26 #h #G #L #T1 #H
  27 @(csx_ind … H) -T1 #T1 #_ #IHT1
  28 elim (cnu_dec_tdeq h G L T1) [ /3 width=4 by ex2_intro, ex_intro/ ] *
  29 #n1 #T0 #HT10 #HnT10
  30 elim (IHT1 … HnT10) -IHT1 -HnT10 [| /2 width=2 by cpm_fwd_cpx/ ]
  31 #T2 * #n2 #HT02 #HT2 /4 width=7 by cpms_step_sn, ex2_intro, ex_intro/
  32 qed-.