matita/matita/contribs/lambda_delta/basic_2/computation/lcprs_lcprs.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/computation/lcprs_cprs.ma".
  16
  17 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS *************)
  18
  19 (* Main properties **********************************************************)
  20
  21 theorem lcprs_trans: ∀L1,L. L1 ⊢ ➡* L → ∀L2. L ⊢ ➡* L2 → L1 ⊢ ➡* L2.
  22 /2 width=3/ qed.
  23
  24 lemma lcprs_pair: ∀L1,L2. L1 ⊢ ➡* L2 → ∀V1,V2. L2 ⊢ V1 ➡* V2 →
  25                   ∀I. L1. ⓑ{I} V1 ⊢ ➡* L2. ⓑ{I} V2.
  26 #L1 #L2 #H @(lcprs_ind … H) -L2 /2 width=1/
  27 #L #L2 #_ #HL2 #IHL1 #V1 #V2 #HV12 #I
  28 @(lcprs_trans … (L.ⓑ{I}V1)) /2 width=1/
  29 qed.