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_feqg.ma".
  17 include "basic_2/rt_computation/fpbs_fqus.ma".
  18
  19 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
  20
  21 (* Properties with extended context-sensitive parallel rt-computation *******)
  22
  23 lemma cpxs_fpbs:
  24       ∀G,L,T1,T2. ❨G,L❩ ⊢ T1 ⬈* T2 → ❨G,L,T1❩ ≥ ❨G,L,T2❩.
  25 #G #L #T1 #T2 #H @(cpxs_ind … H) -T2
  26 /3 width=5 by cpx_fpb, fpbs_strap1/
  27 qed.
  28
  29 lemma fpbs_cpxs_trans:
  30       ∀G1,G,L1,L,T1,T. ❨G1,L1,T1❩ ≥ ❨G,L,T❩ →
  31       ∀T2. ❨G,L❩ ⊢ T ⬈* T2 → ❨G1,L1,T1❩ ≥ ❨G,L,T2❩.
  32 #G1 #G #L1 #L #T1 #T #H1 #T2 #H @(cpxs_ind … H) -T2
  33 /3 width=5 by fpbs_strap1, cpx_fpb/
  34 qed-.
  35
  36 lemma cpxs_fpbs_trans:
  37       ∀G1,G2,L1,L2,T,T2. ❨G1,L1,T❩ ≥ ❨G2,L2,T2❩ →
  38       ∀T1. ❨G1,L1❩ ⊢ T1 ⬈* T → ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩.
  39 #G1 #G2 #L1 #L2 #T #T2 #H1 #T1 #H @(cpxs_ind_dx … H) -T1
  40 /3 width=5 by fpbs_strap2, cpx_fpb/
  41 qed-.
  42
  43 lemma cpxs_teqg_fpbs_trans (S):
  44       reflexive … S → symmetric … S →
  45       ∀G1,L1,T1,T. ❨G1,L1❩ ⊢ T1 ⬈* T → ∀T0. T ≛[S] T0 →
  46       ∀G2,L2,T2. ❨G1,L1,T0❩ ≥ ❨G2,L2,T2❩ → ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩.
  47 /3 width=6 by cpxs_fpbs_trans, teqg_fpbs_trans/ qed-.
  48
  49 lemma cpxs_teqg_fpbs (S):
  50       reflexive … S → symmetric … S →
  51       ∀G,L,T1,T. ❨G,L❩ ⊢ T1 ⬈* T →
  52       ∀T2. T ≛[S] T2 → ❨G,L,T1❩ ≥ ❨G,L,T2❩.
  53 /4 width=5 by cpxs_fpbs_trans, feqg_fpbs, teqg_feqg/ qed.
  54
  55 (* Properties with plus-iterated structural successor for closures **********)
  56
  57 lemma cpxs_fqup_fpbs:
  58       ∀G1,L1,T1,T. ❨G1,L1❩ ⊢ T1 ⬈* T →
  59       ∀G2,L2,T2. ❨G1,L1,T❩ ⬂+ ❨G2,L2,T2❩ → ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩.
  60 /3 width=5 by fpbs_fqup_trans, cpxs_fpbs/ qed.
  61
  62 (* Properties with star-iterated structural successor for closures **********)
  63
  64 lemma cpxs_fqus_fpbs:
  65       ∀G1,L1,T1,T. ❨G1,L1❩ ⊢ T1 ⬈* T →
  66       ∀G2,L2,T2. ❨G1,L1,T❩ ⬂* ❨G2,L2,T2❩ → ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩.
  67 /3 width=5 by fpbs_fqus_trans, cpxs_fpbs/ qed.