matita/matita/contribs/lambdadelta/basic_2/etc/cpr/lfpr.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 notation "hvbox( ⦃ term 46 L1 ⦄ ➡ break ⦃ term 46 L2 ⦄ )"
  16    non associative with precedence 45
  17    for @{ 'FocalizedPRed $L1 $L2 }.
  18
  19 include "basic_2/unfold/ltpss_sn.ma".
  20 include "basic_2/reducibility/ltpr.ma".
  21
  22 (* FOCALIZED PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ***********************)
  23
  24 definition lfpr: relation lenv ≝
  25    λL1,L2. ∃∃L. L1 ➡ L & L ⊢ ▶* [0, |L|] L2
  26 .
  27
  28 interpretation
  29   "focalized parallel reduction (environment)"
  30   'FocalizedPRed L1 L2 = (lfpr L1 L2).
  31
  32 (* Basic properties *********************************************************)
  33
  34 (* Note: lemma 250 *)
  35 lemma lfpr_refl: ∀L. ⦃L⦄ ➡ ⦃L⦄.
  36 /2 width=3/ qed.
  37
  38 lemma ltpss_sn_lfpr: ∀L1,L2,d,e. L1 ⊢ ▶* [d, e] L2 → ⦃L1⦄ ➡ ⦃L2⦄.
  39 /3 width=5/ qed.
  40
  41 lemma ltpr_lfpr: ∀L1,L2. L1 ➡ L2 → ⦃L1⦄ ➡ ⦃L2⦄.
  42 /3 width=3/ qed.
  43
  44 (* Basic inversion lemmas ***************************************************)
  45
  46 lemma lfpr_inv_atom1: ∀L2. ⦃⋆⦄ ➡ ⦃L2⦄ → L2 = ⋆.
  47 #L2 * #L #HL >(ltpr_inv_atom1 … HL) -HL #HL2 >(ltpss_sn_inv_atom1 … HL2) -HL2 //
  48 qed-.