matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpes_cpms.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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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_computation/cprs_cprs.ma".
  16 include "basic_2/rt_equivalence/cpes.ma".
  17
  18 (* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-EQUIVALENCE FOR TERMS **************)
  19
  20 (* Properties with t-bound rt-computation on terms **************************)
  21
  22 lemma cpes_cprs_trans (h) (n) (G) (L) (T0):
  23       ∀T1.  ❪G,L❫ ⊢ T1 ⬌*[h,n,0] T0 →
  24       ∀T2.  ❪G,L❫ ⊢ T0 ➡*[h] T2 → ❪G,L❫ ⊢ T1 ⬌*[h,n,0] T2.
  25 #h #n #G #L #T0 #T1 * #T #HT1 #HT0 #T2 #HT02
  26 elim (cprs_conf … HT0 … HT02) -T0 #T0 #HT0 #HT20
  27 /3 width=3 by cpms_div, cpms_cprs_trans/
  28 qed-.
  29
  30 lemma cpes_cpms_div (h) (n) (n1) (n2) (G) (L) (T0):
  31       ∀T1.  ❪G,L❫ ⊢ T1 ⬌*[h,n,n1] T0 →
  32       ∀T2.  ❪G,L❫ ⊢ T2 ➡*[n2,h] T0 → ❪G,L❫ ⊢ T1 ⬌*[h,n,n2+n1] T2.
  33 #h #n #n1 #n2 #G #L #T0 #T1 * #T #HT1 #HT0 #T2 #HT20
  34 lapply (cpms_trans … HT20 … HT0) -T0 #HT2
  35 /2 width=3 by cpms_div/
  36 qed-.