matita/matita/contribs/lambdadelta/basic_2A/etc/fpbc/fpbc.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/notation/relations/lazybtpredproper_8.ma".
  16 include "basic_2/multiple/fleq.ma".
  17 include "basic_2/reduction/fpbu.ma".
  18
  19 (* "QRST" PROPER PARALLEL REDUCTION FOR CLOSURES ****************************)
  20
  21 definition fpbc: ∀h. sd h → tri_relation genv lenv term ≝
  22                  λh,g,G1,L1,T1,G2,L2,T2.
  23                  ∃∃G,L,T. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G, L, T⦄ & ⦃G, L, T⦄ ≡[0] ⦃G2, L2, T2⦄.
  24
  25 interpretation
  26    "'qrst' proper parallel reduction (closure)"
  27    'LazyBTPRedProper h g G1 L1 T1 G2 L2 T2 = (fpbc h g G1 L1 T1 G2 L2 T2).
  28
  29 (* Baic properties **********************************************************)
  30
  31 lemma fpbu_fpbc: ∀h,g,G1,G2,L1,L2,T1,T2.
  32                  ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≻≡[h, g] ⦃G2, L2, T2⦄.
  33 /2 width=5 by ex2_3_intro/ qed.