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

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  14
  15 include "basic_2/rt_computation/cpxs.ma".
  16 include "basic_2/rt_computation/fpbs_fqup.ma".
  17
  18 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
  19
  20 (* Properties with extended context-sensitive parallel rt-computation *******)
  21
  22 lemma cpxs_fpbs:
  23       ∀G,L,T1,T2. ❪G,L❫ ⊢ T1 ⬈* T2 → ❪G,L,T1❫ ≥ ❪G,L,T2❫.
  24 #G #L #T1 #T2 #H @(cpxs_ind … H) -T2
  25 /3 width=5 by fpbq_cpx, fpbs_strap1/
  26 qed.
  27
  28 lemma fpbs_cpxs_trans:
  29       ∀G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≥ ❪G,L,T❫ →
  30       ∀T2. ❪G,L❫ ⊢ T ⬈* T2 → ❪G1,L1,T1❫ ≥ ❪G,L,T2❫.
  31 #G1 #G #L1 #L #T1 #T #H1 #T2 #H @(cpxs_ind … H) -T2
  32 /3 width=5 by fpbs_strap1, fpbq_cpx/
  33 qed-.
  34
  35 lemma cpxs_fpbs_trans:
  36       ∀G1,G2,L1,L2,T,T2. ❪G1,L1,T❫ ≥ ❪G2,L2,T2❫ →
  37       ∀T1. ❪G1,L1❫ ⊢ T1 ⬈* T → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
  38 #G1 #G2 #L1 #L2 #T #T2 #H1 #T1 #H @(cpxs_ind_dx … H) -T1
  39 /3 width=5 by fpbs_strap2, fpbq_cpx/
  40 qed-.
  41
  42 lemma cpxs_teqx_fpbs_trans:
  43       ∀G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ⬈* T → ∀T0. T ≛ T0 →
  44       ∀G2,L2,T2. ❪G1,L1,T0❫ ≥ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
  45 /3 width=3 by cpxs_fpbs_trans, teqx_fpbs_trans/ qed-.
  46
  47 lemma cpxs_teqx_fpbs:
  48       ∀G,L,T1,T. ❪G,L❫ ⊢ T1 ⬈* T →
  49       ∀T2. T ≛ T2 → ❪G,L,T1❫ ≥ ❪G,L,T2❫.
  50 /4 width=3 by cpxs_fpbs_trans, feqx_fpbs, teqx_feqx/ qed.
  51
  52 (* Properties with star-iterated structural successor for closures **********)
  53
  54 lemma cpxs_fqus_fpbs:
  55       ∀G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ⬈* T →
  56       ∀G2,L2,T2. ❪G1,L1,T❫ ⬂* ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
  57 /3 width=5 by fpbs_fqus_trans, cpxs_fpbs/ qed.
  58
  59 (* Properties with plus-iterated structural successor for closures **********)
  60
  61 lemma cpxs_fqup_fpbs:
  62       ∀G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ⬈* T →
  63       ∀G2,L2,T2. ❪G1,L1,T❫ ⬂+ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
  64 /3 width=5 by fpbs_fqup_trans, cpxs_fpbs/ qed.