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:                                           *)
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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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  14
  15 include "basic_2/reducibility/lcpr_lcpr.ma".
  16 include "basic_2/computation/lcprs_cprs.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS *************)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 lemma lcprs_strip: ∀L,L1. L ⊢ ➡* L1 → ∀L2. L ⊢ ➡ L2 →
  23                    ∃∃L0. L1 ⊢ ➡ L0 & L2 ⊢ ➡* L0.
  24 /3 width=3/ qed.
  25
  26 (* Main properties **********************************************************)
  27
  28 theorem lcprs_conf: ∀L,L1. L ⊢ ➡* L1 → ∀L2. L ⊢ ➡* L2 →
  29                     ∃∃L0. L1 ⊢ ➡* L0 & L2 ⊢ ➡* L0.
  30 /3 width=3/ qed.
  31
  32 theorem lcprs_trans: ∀L1,L. L1 ⊢ ➡* L → ∀L2. L ⊢ ➡* L2 → L1 ⊢ ➡* L2.
  33 /2 width=3/ qed.
  34
  35 lemma lcprs_pair: ∀L1,L2. L1 ⊢ ➡* L2 → ∀V1,V2. L2 ⊢ V1 ➡* V2 →
  36                   ∀I. L1. ⓑ{I} V1 ⊢ ➡* L2. ⓑ{I} V2.
  37 #L1 #L2 #H @(lcprs_ind … H) -L2 /2 width=1/
  38 #L #L2 #_ #HL2 #IHL1 #V1 #V2 #HV12 #I
  39 @(lcprs_trans … (L.ⓑ{I}V1)) /2 width=1/
  40 qed.