matita/matita/contribs/lambdadelta/basic_2A/computation/cpre.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_2A/notation/relations/predeval_4.ma".
  16 include "basic_2A/computation/cprs.ma".
  17 include "basic_2A/computation/csx.ma".
  18
  19 (* EVALUATION FOR CONTEXT-SENSITIVE PARALLEL REDUCTION ON TERMS *************)
  20
  21 definition cpre: relation4 genv lenv term term ≝
  22                  λG,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 ∧ ⦃G, L⦄ ⊢ ➡ 𝐍⦃T2⦄.
  23
  24 interpretation "evaluation for context-sensitive parallel reduction (term)"
  25    'PRedEval G L T1 T2 = (cpre G L T1 T2).
  26
  27 (* Basic properties *********************************************************)
  28
  29 (* Basic_1: was just: nf2_sn3 *)
  30 lemma csx_cpre: ∀h,g,G,L,T1. ⦃G, L⦄ ⊢ ⬊*[h, g] T1 → ∃T2. ⦃G, L⦄ ⊢ T1 ➡* 𝐍⦃T2⦄.
  31 #h #g #G #L #T1 #H @(csx_ind … H) -T1
  32 #T1 #_ #IHT1 elim (cnr_dec G L T1) /3 width=3 by ex_intro, conj/
  33 * #T #H1T1 #H2T1 elim (IHT1 … H2T1) -IHT1 -H2T1 /2 width=2 by cpr_cpx/
  34 #T2 * /4 width=3 by cprs_strap2, ex_intro, conj/
  35 qed.