matita/matita/contribs/lambdadelta/basic_2/etc/ssta1/fpbs_lift.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/reduction/fpb_lift.ma".
  16 include "basic_2/computation/cpxs_lift.ma".
  17 include "basic_2/computation/fpbs.ma".
  18
  19 (* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
  20
  21 (* Advanced properties ******************************************************)
  22
  23 lemma lsstas_fpbs: ∀h,g,G,L,T1,T2,l2. ⦃G, L⦄ ⊢ T1 •*[h, g, l2] T2 →
  24                    ∀l1. l2 ≤ l1 → ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 → ⦃G, L, T1⦄ ≥[h, g] ⦃G, L, T2⦄.
  25 /3 width=5 by cpxs_fpbs, lsstas_cpxs/ qed.
  26
  27 lemma ssta_fpbs: ∀h,g,G,L,T,U,l.
  28                  ⦃G, L⦄ ⊢ T ▪[h, g] l+1 → ⦃G, L⦄ ⊢ T •[h, g] U →
  29                  ⦃G, L, T⦄ ≥[h, g] ⦃G, L, U⦄.
  30 /4 width=2 by fpb_fpbs, ssta_fpb/ qed.
  31
  32 (* Note: this is used in the closure proof *)
  33 lemma cpr_lpr_ssta_fpbs: ∀h,g,G,L1,L2,T1,T2,U2,l2.
  34                          ⦃G, L1⦄ ⊢ T1 ➡ T2 → ⦃G, L1⦄ ⊢ ➡ L2 →
  35                          ⦃G, L2⦄ ⊢ T2 ▪[h, g] l2+1 → ⦃G, L2⦄ ⊢ T2 •[h, g] U2 →
  36                          ⦃G, L1, T1⦄ ≥[h, g] ⦃G, L2, U2⦄.
  37 /4 width=5 by fpbs_strap1, cpr_lpr_fpbs, ssta_cpx, fpb_cpx/ qed.