matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpmuwe_cpmre.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 include "basic_2/rt_computation/cpmre_aaa.ma".
  16 include "basic_2/rt_computation/cnuw_cnuw.ma".
  17 include "basic_2/rt_computation/cpmuwe.ma".
  18 include "basic_2/dynamic/cnv_cpmre.ma".
  19
  20 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
  21
  22 (* Advanced Properties with t-unbound whd evaluation on terms ***************)
  23
  24 lemma cnv_R_cpmuwe_dec (h) (a) (G) (L):
  25       ∀T. ❪G,L❫ ⊢ T ![h,a] → ∀n. Decidable (R_cpmuwe h G L T n).
  26 #h #a #G #L #T1 #HT1 #n
  27 elim (cnv_fwd_aaa … HT1) #A #HA
  28 elim (cpmre_total_aaa h n … HA) -HA #T2 #HT12
  29 elim (cnuw_dec h G L T2) #HnT1
  30 [ /5 width=3 by cpmre_fwd_cpms, cpmuwe_intro, ex_intro, or_introl/
  31 | @or_intror * #T3 * #HT13 #HT3
  32   lapply (cnv_cpmre_cpms_conf … HT1 … HT13 … HT12) -a -T1 #HT32
  33   /4 width=9 by cpmre_fwd_cpms, cnuw_cpms_trans/
  34 ]
  35 qed-.