matita/matita/contribs/lambda_delta/Basic_2/computation/cprs_cprs.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 "Basic_2/reducibility/cpr_cpr.ma".
  16 include "Basic_2/computation/cprs_lcpr.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
  19
  20 (* Main propertis ***********************************************************)
  21
  22 (* Basic_1: was: pr3_t *)
  23 theorem cprs_trans: ∀L,T1,T. L ⊢ T1 ➡* T → ∀T2. L ⊢ T ➡* T2 → L ⊢ T1 ➡* T2.
  24 /2 width=3/ qed.
  25
  26 (* Basic_1: was: pr3_confluence *)
  27 theorem cprs_conf: ∀L,T1,T. L ⊢ T ➡* T1 → ∀T2. L ⊢ T ➡* T2 →
  28                    ∃∃T0. L ⊢ T1 ➡* T0 & L ⊢ T2 ➡* T0.
  29 /3 width=3/ qed.
  30
  31 (* Advanced properties ******************************************************)
  32
  33 (* Basic_1: was only: pr3_pr2_pr3_t *)
  34 lemma lcpr_cprs_trans: ∀L1,L2. L1 ⊢ ➡ L2 →
  35                        ∀T1,T2. L2 ⊢ T1 ➡* T2 → L1 ⊢ T1 ➡* T2.
  36 #L1 #L2 #HL12 #T1 #T2 #H @(cprs_ind … H) -T2 //
  37 #T #T2 #_ #HT2 #IHT2 /3 width=5/
  38 qed.