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

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  14
  15 include "basic_2/static/ffdeq_fqup.ma".
  16 include "basic_2/rt_computation/cpxs.ma".
  17 include "basic_2/rt_computation/fpbs_fqup.ma".
  18
  19 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
  20
  21 (* Properties with uncounted context-sensitive parallel rt-computation ******)
  22
  23 lemma cpxs_fpbs: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → ⦃G, L, T1⦄ ≥[h, o] ⦃G, L, T2⦄.
  24 #h #o #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: ∀h,o,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G, L, T⦄ →
  29                        ∀T2. ⦃G, L⦄ ⊢ T ⬈*[h] T2 → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G, L, T2⦄.
  30 #h #o #G1 #G #L1 #L #T1 #T #H1 #T2 #H @(cpxs_ind … H) -T2
  31 /3 width=5 by fpbs_strap1, fpbq_cpx/
  32 qed-.
  33
  34 lemma cpxs_fpbs_trans: ∀h,o,G1,G2,L1,L2,T,T2. ⦃G1, L1, T⦄ ≥[h, o] ⦃G2, L2, T2⦄ →
  35                        ∀T1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
  36 #h #o #G1 #G2 #L1 #L2 #T #T2 #H1 #T1 #H @(cpxs_ind_dx … H) -T1
  37 /3 width=5 by fpbs_strap2, fpbq_cpx/
  38 qed-.
  39
  40 lemma cpxs_tdeq_fpbs: ∀h,o,G,L,T1,T. ⦃G, L⦄ ⊢ T1 ⬈*[h] T →
  41                       ∀T2. T ≛[h, o] T2 → ⦃G, L, T1⦄ ≥[h, o] ⦃G, L, T2⦄.
  42 /4 width=3 by cpxs_fpbs_trans, ffdeq_fpbs, tdeq_ffdeq/ qed.
  43
  44 (* Properties with star-iterated structural successor for closures **********)
  45
  46 lemma cpxs_fqus_fpbs: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
  47                       ∀G2,L2,T2. ⦃G1, L1, T⦄ ⊐* ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
  48 /3 width=5 by fpbs_fqus_trans, cpxs_fpbs/ qed.
  49
  50 (* Properties with plus-iterated structural successor for closures **********)
  51
  52 lemma cpxs_fqup_fpbs: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
  53                       ∀G2,L2,T2. ⦃G1, L1, T⦄ ⊐+ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
  54 /3 width=5 by fpbs_fqup_trans, cpxs_fpbs/ qed.