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

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  14
  15 include "ground/lib/star.ma".
  16 include "basic_2/notation/relations/predsubtystar_6.ma".
  17 include "basic_2/rt_transition/fpb.ma".
  18
  19 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
  20
  21 definition fpbs: tri_relation genv lenv term ≝
  22            tri_TC … fpb.
  23
  24 interpretation
  25   "parallel rst-computation (closure)"
  26   'PRedSubTyStar  G1 L1 T1 G2 L2 T2 = (fpbs G1 L1 T1 G2 L2 T2).
  27
  28
  29 (* Basic properties *********************************************************)
  30
  31 (* Basic_2A1: uses: fpbq_fpbs *)
  32 lemma fpb_fpbs:
  33       ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫ →
  34       ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
  35 /2 width=1 by tri_inj/ qed.
  36
  37 lemma fpbs_strap1:
  38       ∀G1,G,G2,L1,L,L2,T1,T,T2. ❪G1,L1,T1❫ ≥ ❪G,L,T❫ →
  39       ❪G,L,T❫ ≽ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
  40 /2 width=5 by tri_step/ qed-.
  41
  42 lemma fpbs_strap2:
  43       ∀G1,G,G2,L1,L,L2,T1,T,T2. ❪G1,L1,T1❫ ≽ ❪G,L,T❫ →
  44       ❪G,L,T❫ ≥ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
  45 /2 width=5 by tri_TC_strap/ qed-.
  46
  47 (* Basic_2A1: removed theorems 3:
  48               fpb_fpbsa_trans fpbs_fpbsa fpbsa_inv_fpbs
  49 *)