matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_fqup.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 "static_2/s_computation/fqus_fqup.ma".
  16 include "static_2/static/feqx_fqup.ma".
  17 include "basic_2/rt_computation/fpbs_fqus.ma".
  18
  19 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
  20
  21 (* Advanced properties ******************************************************)
  22
  23 lemma teqx_fpbs_trans:
  24       ∀T1,T. T1 ≛ T →
  25       ∀G1,G2,L1,L2,T2. ❪G1,L1,T❫ ≥ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
  26 /3 width=5 by feqx_fpbs_trans, teqx_feqx/ qed-.
  27
  28 lemma fpbs_teqx_trans:
  29       ∀G1,G2,L1,L2,T1,T. ❪G1,L1,T1❫ ≥ ❪G2,L2,T❫ →
  30       ∀T2. T ≛ T2 → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
  31 /3 width=5 by fpbs_feqx_trans, teqx_feqx/ qed-.
  32
  33 (* Properties with plus-iterated structural successor for closures **********)
  34
  35 lemma fqup_fpbs:
  36       ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂+ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
  37 #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
  38 /4 width=5 by fqu_fquq, fpbq_fquq, tri_step/
  39 qed.
  40
  41 lemma fpbs_fqup_trans:
  42       ∀G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≥ ❪G,L,T❫ →
  43       ∀G2,L2,T2. ❪G,L,T❫ ⬂+ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
  44 /3 width=5 by fpbs_fqus_trans, fqup_fqus/ qed-.
  45
  46 lemma fqup_fpbs_trans:
  47       ∀G,G2,L,L2,T,T2. ❪G,L,T❫ ≥ ❪G2,L2,T2❫ →
  48       ∀G1,L1,T1. ❪G1,L1,T1❫ ⬂+ ❪G,L,T❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
  49 /3 width=5 by fqus_fpbs_trans, fqup_fqus/ qed-.