matita/matita/contribs/lambdadelta/basic_2/etc_2A1/fpbc/fpbg_fpbg.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/computation/fpbs_fpbu.ma".
  16 include "basic_2/computation/fpbs_fpbc.ma".
  17 include "basic_2/computation/fpbs_fpbs.ma".
  18 include "basic_2/computation/fpbg_fpbs.ma".
  19
  20 (* "QRST" PROPER PARALLEL COMPUTATION FOR CLOSURES **************************)
  21
  22 (* Advanced inversion lemmas ************************************************)
  23
  24 lemma fpbg_inv_fpbu_sn: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄ →
  25                         ∃∃G,L,T. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G, L, T⦄ & ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄.
  26 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbg_ind_dx … H) -G1 -L1 -T1
  27 [ #G1 #L1 #T1 * /3 width=5 by fleq_fpbs, ex2_3_intro/
  28 | #G1 #G #L1 #L #T1 #T *
  29   #G0 #L0 #T0 #H10 #H0 #_ *
  30   /5 width=9 by fpbu_fpbs, fpbs_trans, fleq_fpbs, ex2_3_intro/
  31 ]
  32 qed-.
  33
  34 (* Advanced forward lemmas **************************************************)
  35
  36 lemma fpbg_fwd_fpbs: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄ →
  37                      ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
  38 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbg_ind … H) -G2 -L2 -T2
  39 [2: #G #G2 #L #L2 #T #T2 #_ #H2 #IH1 @(fpbs_trans … IH1) -IH1 ] (**) (* full auto fails *)
  40 /2 width=1 by fpbc_fpbs/
  41 qed-.
  42
  43 (* Advanced properties ******************************************************)
  44
  45 lemma fpbs_fpbu_trans: ∀h,g,F1,F2,K1,K2,T1,T2. ⦃F1, K1, T1⦄ ≥[h, g] ⦃F2, K2, T2⦄ →
  46                        ∀G2,L2,U2. ⦃F2, K2, T2⦄ ≻[h, g] ⦃G2, L2, U2⦄ →
  47                        ∃∃G1,L1,U1. ⦃F1, K1, T1⦄ ≻[h, g] ⦃G1, L1, U1⦄ & ⦃G1, L1, U1⦄ ≥[h, g] ⦃G2, L2, U2⦄.
  48 /5 width=5 by fpbg_inv_fpbu_sn, fpbs_fpbg_trans, fpbc_fpbg, fpbu_fpbc/ qed-.
  49
  50 (* Man properties ***********************************************************)
  51
  52 theorem fpbg_trans: ∀h,g. tri_transitive … (fpbg h g).
  53 /2 width=5 by tri_TC_transitive/ qed-.