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 unbound context-sensitive parallel rt-computation ********)
  21
  22 lemma cpxs_fpbs: ∀h,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → ⦃G, L, T1⦄ ≥[h] ⦃G, L, T2⦄.
  23 #h #G #L #T1 #T2 #H @(cpxs_ind … H) -T2
  24 /3 width=5 by fpbq_cpx, fpbs_strap1/
  25 qed.
  26
  27 lemma fpbs_cpxs_trans: ∀h,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≥[h] ⦃G, L, T⦄ →
  28                        ∀T2. ⦃G, L⦄ ⊢ T ⬈*[h] T2 → ⦃G1, L1, T1⦄ ≥[h] ⦃G, L, T2⦄.
  29 #h #G1 #G #L1 #L #T1 #T #H1 #T2 #H @(cpxs_ind … H) -T2
  30 /3 width=5 by fpbs_strap1, fpbq_cpx/
  31 qed-.
  32
  33 lemma cpxs_fpbs_trans: ∀h,G1,G2,L1,L2,T,T2. ⦃G1, L1, T⦄ ≥[h] ⦃G2, L2, T2⦄ →
  34                        ∀T1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T → ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄.
  35 #h #G1 #G2 #L1 #L2 #T #T2 #H1 #T1 #H @(cpxs_ind_dx … H) -T1
  36 /3 width=5 by fpbs_strap2, fpbq_cpx/
  37 qed-.
  38
  39 lemma cpxs_tdeq_fpbs_trans: ∀h,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
  40                             ∀T0. T ≛ T0 →
  41                             ∀G2,L2,T2. ⦃G1, L1, T0⦄ ≥[h] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄.
  42 /3 width=3 by cpxs_fpbs_trans, tdeq_fpbs_trans/ qed-.
  43
  44 lemma cpxs_tdeq_fpbs: ∀h,G,L,T1,T. ⦃G, L⦄ ⊢ T1 ⬈*[h] T →
  45                       ∀T2. T ≛ T2 → ⦃G, L, T1⦄ ≥[h] ⦃G, L, T2⦄.
  46 /4 width=3 by cpxs_fpbs_trans, fdeq_fpbs, tdeq_fdeq/ qed.
  47
  48 (* Properties with star-iterated structural successor for closures **********)
  49
  50 lemma cpxs_fqus_fpbs: ∀h,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
  51                       ∀G2,L2,T2. ⦃G1, L1, T⦄ ⊐* ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄.
  52 /3 width=5 by fpbs_fqus_trans, cpxs_fpbs/ qed.
  53
  54 (* Properties with plus-iterated structural successor for closures **********)
  55
  56 lemma cpxs_fqup_fpbs: ∀h,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
  57                       ∀G2,L2,T2. ⦃G1, L1, T⦄ ⊐+ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄.
  58 /3 width=5 by fpbs_fqup_trans, cpxs_fpbs/ qed.