matita/matita/contribs/lambda_delta/basic_2/computation/fprs.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/fpr.ma".
  16
  17 (* CONTEXT-FREE PARALLEL COMPUTATION ON CLOSURES ****************************)
  18
  19 definition fprs: bi_relation lenv term ≝ bi_TC … fpr.
  20
  21 interpretation "context-free parallel computation (closure)"
  22    'FocalizedPRedStar L1 T1 L2 T2 = (fprs L1 T1 L2 T2).
  23
  24 (* Basic eliminators ********************************************************)
  25
  26 lemma fprs_ind: ∀L1,T1. ∀R:relation2 lenv term. R L1 T1 →
  27                 (∀L,L2,T,T2. ⦃L1, T1⦄ ➡* ⦃L, T⦄ → ⦃L, T⦄ ➡ ⦃L2, T2⦄ → R L T → R L2 T2) →
  28                 ∀L2,T2. ⦃L1, T1⦄ ➡* ⦃L2, T2⦄ → R L2 T2.
  29 /3 width=7 by bi_TC_star_ind/ qed-.
  30
  31 lemma fprs_ind_dx: ∀L2,T2. ∀R:relation2 lenv term. R L2 T2 →
  32                    (∀L1,L,T1,T. ⦃L1, T1⦄ ➡ ⦃L, T⦄ → ⦃L, T⦄ ➡* ⦃L2, T2⦄ → R L T → R L1 T1) →
  33                    ∀L1,T1. ⦃L1, T1⦄ ➡* ⦃L2, T2⦄ → R L1 T1.
  34 /3 width=7 by bi_TC_star_ind_dx/ qed-.
  35
  36 (* Basic properties *********************************************************)
  37
  38 lemma fprs_refl: bi_reflexive … fprs.
  39 /2 width=1/ qed.
  40
  41 lemma fprs_strap1: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ ➡* ⦃L, T⦄ → ⦃L, T⦄ ➡ ⦃L2, T2⦄ →
  42                    ⦃L1, T1⦄ ➡* ⦃L2, T2⦄.
  43 /2 width=4/ qed.
  44
  45 lemma fprs_strap2: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ ➡ ⦃L, T⦄ → ⦃L, T⦄ ➡* ⦃L2, T2⦄ →
  46                    ⦃L1, T1⦄ ➡* ⦃L2, T2⦄.
  47 /2 width=4/ qed.