matita/matita/contribs/lambdadelta/basic_2/reduction/fpbu.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/notation/relations/btpredproper_8.ma".
  16 include "basic_2/reduction/fpb.ma".
  17
  18 (* "RST" PROPER PARALLEL COMPUTATION FOR CLOSURES ***************************)
  19
  20 inductive fpbu (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
  21 | fpbu_fqu: ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → fpbu h g G1 L1 T1 G2 L2 T2
  22 | fpbu_cpx: ∀T2. ⦃G1, L1⦄ ⊢ T1 ➡[h, g] T2 → (T1 = T2 → ⊥) → fpbu h g G1 L1 T1 G1 L1 T2
  23 | fpbu_lpx: ∀L2. ⦃G1, L1⦄ ⊢ ➡[h, g] L2 → (L1 ≡[T1, 0] L2 → ⊥) → fpbu h g G1 L1 T1 G1 L2 T1
  24 .
  25
  26 interpretation
  27    "'rst' proper parallel reduction (closure)"
  28    'BTPRedProper h g G1 L1 T1 G2 L2 T2 = (fpbu h g G1 L1 T1 G2 L2 T2).
  29
  30 (* Basic properties *********************************************************)
  31
  32 lemma cpr_fpbu: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → (T1 = T2 → ⊥) →
  33                 ⦃G, L, T1⦄ ≻[h, g] ⦃G, L, T2⦄.
  34 /3 width=1 by fpbu_cpx, cpr_cpx/ qed.
  35
  36 lemma lpr_fpbu: ∀h,g,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡ L2 → (L1 ≡[T, 0] L2 → ⊥) →
  37                 ⦃G, L1, T⦄ ≻[h, g] ⦃G, L2, T⦄.
  38 /3 width=1 by fpbu_lpx, lpr_lpx/ qed.
  39
  40 (* Basic forward lemmas *****************************************************)
  41
  42 lemma fpbu_fwd_fpb: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ →
  43                     ⦃G1, L1, T1⦄ ≽[h, g] ⦃G2, L2, T2⦄.
  44 #h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
  45 /3 width=1 by fpb_fquq, fpb_cpx, fpb_lpx, fqu_fquq/
  46 qed-.