matita/matita/contribs/lambdadelta/basic_2A/computation/fpbg.ma

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  14
  15 include "basic_2A/notation/relations/lazybtpredstarproper_8.ma".
  16 include "basic_2A/reduction/fpb.ma".
  17 include "basic_2A/computation/fpbs.ma".
  18
  19 (* "QRST" PROPER PARALLEL COMPUTATION FOR CLOSURES **************************)
  20
  21 definition fpbg: ∀h. sd h → tri_relation genv lenv term ≝
  22                  λh,g,G1,L1,T1,G2,L2,T2.
  23                  ∃∃G,L,T. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G, L, T⦄ & ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄.
  24
  25 interpretation "'qrst' proper parallel computation (closure)"
  26    'LazyBTPRedStarProper h g G1 L1 T1 G2 L2 T2 = (fpbg h g G1 L1 T1 G2 L2 T2).
  27
  28 (* Basic properties *********************************************************)
  29
  30 lemma fpb_fpbg: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ →
  31                 ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
  32 /2 width=5 by ex2_3_intro/ qed.
  33
  34 lemma fpbg_fpbq_trans: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2.
  35                        ⦃G1, L1, T1⦄ >≡[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ ≽[h, g] ⦃G2, L2, T2⦄ →
  36                        ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
  37 #h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 *
  38 /3 width=9 by fpbs_strap1, ex2_3_intro/
  39 qed-.