matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpmuwe_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 "static_2/syntax/tweq_teqx.ma".
  16 include "basic_2/rt_computation/csx_cpxs.ma".
  17 include "basic_2/rt_computation/cpms_cpxs.ma".
  18 include "basic_2/rt_computation/cnuw_cnuw.ma".
  19 include "basic_2/rt_computation/cpmuwe.ma".
  20
  21 (* T-UNBOUND WHD EVALUATION FOR T-BOUND RT-TRANSITION ON TERMS **************)
  22
  23 (* Properties with strong normalization for unbound rt-transition for terms *)
  24
  25 lemma cpmuwe_total_csx (h) (G) (L):
  26       ∀T1. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T1❫ → ∃∃T2,n. ❪G,L❫ ⊢ T1 ➡*𝐍𝐖*[h,n] T2.
  27 #h #G #L #T1 #H
  28 @(csx_ind_cpxs … H) -T1 #T1 #_ #IHT1
  29 elim (cnuw_dec_ex h G L T1)
  30 [ -IHT1 #HT1 /3 width=4 by cpmuwe_intro, ex1_2_intro/
  31 | * #n1 #T0 #HT10 #HnT10
  32   elim (IHT1 … T0) -IHT1
  33   [ #T2 #n2 * #HT02 #HT2 /4 width=5 by cpms_trans, cpmuwe_intro, ex1_2_intro/
  34   | /3 width=1 by teqx_tweq/
  35   | /2 width=2 by cpms_fwd_cpxs/
  36   ]
  37 ]
  38 qed-.
  39
  40 lemma R_cpmuwe_total_csx (h) (G) (L):
  41       ∀T1. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T1❫ → ∃n. R_cpmuwe h G L T1 n.
  42 #h #G #L #T1 #H
  43 elim (cpmuwe_total_csx … H) -H #T2 #n #HT12
  44 /3 width=3 by ex_intro (* 2x *)/
  45 qed-.