matita/matita/contribs/lambdadelta/basic_2/reduction/fpbu_fleq.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/multiple/fleq.ma".
  16 include "basic_2/reduction/fpbu_lleq.ma".
  17
  18 (* "RST" PROPER PARALLEL COMPUTATION FOR CLOSURES ***************************)
  19
  20 (* Properties on lazy equivalence for closures ******************************)
  21
  22 lemma fleq_fpbu_trans: ∀h,g,F1,F2,K1,K2,T1,T2. ⦃F1, K1, T1⦄ ≡[0] ⦃F2, K2, T2⦄ →
  23                        ∀G2,L2,U2. ⦃F2, K2, T2⦄ ≻[h, g] ⦃G2, L2, U2⦄ →
  24                        ∃∃G1,L1,U1. ⦃F1, K1, T1⦄ ≻[h, g] ⦃G1, L1, U1⦄ & ⦃G1, L1, U1⦄ ≡[0] ⦃G2, L2, U2⦄.
  25 #h #g #F1 #F2 #K1 #K2 #T1 #T2 * -F2 -K2 -T2
  26 #K2 #HK12 #G2 #L2 #U2 #H12 elim (lleq_fpbu_trans … HK12 … H12) -K2
  27 /3 width=5 by fleq_intro, ex2_3_intro/
  28 qed-.
  29
  30 lemma fpb_fpbu: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≽[h, g] ⦃G2, L2, T2⦄ →
  31                 ⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ ∨
  32                 ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄.
  33 #h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
  34 [ #G2 #L2 #T2 #H elim (fquq_inv_gen … H) -H
  35   [ /3 width=1 by fpbu_fqu, or_intror/
  36   | * #H1 #H2 #H3 destruct /2 width=1 by or_introl/
  37   ]
  38 | #T2 #HT12 elim (eq_term_dec T1 T2)
  39   #HnT12 destruct /4 width=1 by fpbu_cpx, or_intror, or_introl/
  40 | #L2 #HL12 elim (lleq_dec … T1 L1 L2 0)
  41   /4 width=1 by fpbu_lpx, fleq_intro, or_intror, or_introl/
  42 | /3 width=1 by fleq_intro, or_introl/
  43 ]
  44 qed-.