matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_fqus.ma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
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  14
  15 include "static_2/s_computation/fqus.ma".
  16 include "basic_2/rt_computation/fpbs.ma".
  17
  18 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
  19
  20 (* Properties with star-iterated structural successor for closures **********)
  21
  22 lemma fqus_fpbs:
  23       ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂* ❪G2,L2,T2❫ →
  24       ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
  25 #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqus_ind … H) -G2 -L2 -T2
  26 /3 width=5 by fpbq_fquq, tri_step/
  27 qed.
  28
  29 lemma fpbs_fqus_trans:
  30       ∀G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≥ ❪G,L,T❫ →
  31       ∀G2,L2,T2. ❪G,L,T❫ ⬂* ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
  32 #G1 #G #L1 #L #T1 #T #H1 #G2 #L2 #T2 #H @(fqus_ind … H) -G2 -L2 -T2
  33 /3 width=5 by fpbs_strap1, fpbq_fquq/
  34 qed-.
  35
  36 lemma fqus_fpbs_trans:
  37       ∀G,G2,L,L2,T,T2. ❪G,L,T❫ ≥ ❪G2,L2,T2❫ →
  38       ∀G1,L1,T1. ❪G1,L1,T1❫ ⬂* ❪G,L,T❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
  39 #G #G2 #L #L2 #T #T2 #H1 #G1 #L1 #T1 #H @(fqus_ind_dx … H) -G1 -L1 -T1
  40 /3 width=5 by fpbs_strap2, fpbq_fquq/
  41 qed-.