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:                                           *)
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   8 (*      ||A||         http://helm.cs.unibo.it                             *)
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  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_computation/csx.ma".
  17 include "basic_2/rt_computation/cnuw_tdeq.ma".
  18 include "basic_2/rt_computation/cpmuwe.ma".
  19
  20 (* T-UNBOUND WHD EVALUATION FOR T-BOUND RT-TRANSITION ON TERMS **************)
  21
  22 (* Properties with strong normalization for unbound rt-transition for terms *)
  23
  24 lemma cpmuwe_total_csx (h) (G) (L):
  25       ∀T1. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ → ∃∃T2,n. ⦃G,L⦄ ⊢ T1 ➡*𝐍𝐖*[h,n] T2.
  26 #h #G #L #T1 #H
  27 @(csx_ind … H) -T1 #T1 #_ #IHT1
  28 elim (cnuw_dec_tdeq h G L T1)
  29 [ -IHT1 #HT1 /3 width=4 by cpmuwe_intro, ex1_2_intro/
  30 | * #n1 #T0 #HT10 #HnT10
  31   elim (IHT1 … HnT10) -IHT1 -HnT10 [| /2 width=2 by cpm_fwd_cpx/ ]
  32   #T2 #n2 * #HT02 #HT2 /4 width=5 by cpms_step_sn, cpmuwe_intro, ex1_2_intro/
  33 ]
  34 qed-.
  35
  36 lemma R_cpmuwe_total_csx (h) (G) (L):
  37       ∀T1. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ → ∃n. R_cpmuwe h G L T1 n.
  38 #h #G #L #T1 #H
  39 elim (cpmuwe_total_csx … H) -H #T2 #n #HT12
  40 /3 width=3 by ex_intro (* 2x *)/
  41 qed-.