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

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  14
  15 include "basic_2/rt_computation/fpbg_fqup.ma".
  16 include "basic_2/rt_computation/fpbg_cpxs.ma".
  17 include "basic_2/rt_computation/cpms_fpbs.ma".
  18
  19 (* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
  20
  21 (* Forward lemmas with proper parallel rst-computation for closures *********)
  22
  23 lemma cpms_tdneq_fwd_fpbg (h) (n):
  24       ∀G,L,T1,T2. ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2 →
  25       (T1 ≛ T2 → ⊥) → ⦃G,L,T1⦄ >[h] ⦃G,L,T2⦄.
  26 /3 width=2 by cpms_fwd_cpxs, cpxs_tdneq_fpbg/ qed-.
  27
  28 lemma fpbg_cpms_trans (h) (n):
  29       ∀G1,G2,L1,L2,T1,T. ⦃G1, L1, T1⦄ >[h] ⦃G2, L2, T⦄ →
  30       ∀T2. ⦃G2, L2⦄ ⊢ T ➡*[n,h] T2 → ⦃G1, L1, T1⦄ >[h] ⦃G2, L2, T2⦄.
  31 /3 width=5 by fpbg_fpbs_trans, cpms_fwd_fpbs/ qed-.
  32
  33 lemma cpms_fpbg_trans (h) (n):
  34       ∀G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ➡*[n,h] T →
  35       ∀G2,L2,T2. ⦃G1, L1, T⦄ >[h] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h] ⦃G2, L2, T2⦄.
  36 /3 width=5 by fpbs_fpbg_trans, cpms_fwd_fpbs/ qed-.
  37
  38 lemma fqup_cpms_fwd_fpbg (h):
  39       ∀G1,G2,L1,L2,T1,T. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T⦄ →
  40       ∀n,T2. ⦃G2, L2⦄ ⊢ T ➡*[n,h] T2 → ⦃G1, L1, T1⦄ >[h] ⦃G2, L2, T2⦄.
  41 /3 width=5 by cpms_fwd_fpbs, fqup_fpbg,fpbg_fpbs_trans/ qed-.
  42
  43 lemma cpm_tdneq_cpm_cpms_tdeq_sym_fwd_fpbg (h) (G) (L) (T1):
  44       ∀n1,T. ⦃G,L⦄ ⊢ T1 ➡[n1,h] T → (T1 ≛ T → ⊥) →
  45       ∀n2,T2. ⦃G,L⦄⊢ T ➡*[n2,h] T2 → T1 ≛ T2 → ⦃G,L,T1⦄ >[h] ⦃G,L,T1⦄.
  46 #h #G #L #T1 #n1 #T #H1T1 #H2T1 #n2 #T2 #H1T2 #H2T12
  47 /4 width=7 by cpms_fwd_fpbs, cpm_fpb, fpbs_tdeq_trans, tdeq_sym, ex2_3_intro/
  48 qed-.