matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/cprs_tpss.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                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "basic_2/reducibility/cpr_tpss.ma".
  16 include "basic_2/computation/cprs.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
  19
  20 (* Properties on partial unfold for terms ***********************************)
  21
  22 lemma cprs_tpss_trans: ∀L,T1,T. L ⊢ T1 ➡* T →
  23                        ∀T2,d,e. L ⊢ T ▶* [d, e] T2 → L ⊢ T1 ➡* T2.
  24 #L #T1 #T #H @(cprs_ind … H) -T /2 width=3/ /3 width=5/
  25 qed.
  26
  27 lemma cprs_tps_trans: ∀L,T1,T. L ⊢ T1 ➡* T →
  28                       ∀T2,d,e. L ⊢ T ▶ [d, e] T2 → L ⊢ T1 ➡* T2.
  29 /3 width=5 by inj, cprs_tpss_trans/ qed. (**) (* auto too slow without trace *)
  30
  31 lemma cprs_tpss_conf: ∀L,T0,T1. L ⊢ T0 ➡* T1 →
  32                       ∀T2,d,e. L ⊢ T0 ▶* [d, e] T2 →
  33                       ∃∃T. L ⊢ T1 ▶* [d, e] T & L ⊢ T2 ➡* T.
  34 #L #T0 #T1 #H @(cprs_ind … H) -T1 /2 width=3/
  35 #T #T1 #_ #HT1 #IHT0 #T2 #d #e #HT02
  36 elim (IHT0 … HT02) -T0 #T0 #HT0 #HT20
  37 elim (cpr_tpss_conf … HT1 … HT0) -T /3 width=5/
  38 qed-.