matita/matita/contribs/lambdadelta/basic_2/etc/lpc/lfpc.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 @{ 'FocalizedPConvAlt $L1 $L2 }.
  18
  19 include "basic_2/reducibility/lfpr.ma".
  20
  21 (* FOCALIZED PARALLEL CONVERSION ON LOCAL ENVIRONMENTS **********************)
  22
  23 definition lfpc: relation lenv ≝
  24    λL1,L2. ⦃L1⦄ ➡ ⦃L2⦄ ∨ ⦃L2⦄ ➡ ⦃L1⦄.
  25
  26 interpretation
  27    "focalized parallel conversion (local environment)"
  28    'FocalizedPConv L1 L2 = (lfpc L1 L2).
  29
  30 (* Basic properties *********************************************************)
  31
  32 lemma lfpc_refl: ∀L. ⦃L⦄ ⬌ ⦃L⦄.
  33 /2 width=1/ qed.
  34
  35 lemma lfpc_sym: ∀L1,L2. ⦃L1⦄ ⬌ ⦃L2⦄ → ⦃L2⦄ ⬌ ⦃L1⦄.
  36 #L1 #L2 * /2 width=1/
  37 qed.
  38
  39 lemma lfpc_lfpr: ∀L1,L2. ⦃L1⦄ ⬌ ⦃L2⦄ → ∃∃L. ⦃L1⦄ ➡ ⦃L⦄ & ⦃L2⦄ ➡ ⦃L⦄.
  40 #L1 #L2 * /2 width=3/
  41 qed.