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14
15 include "basic_2/notation/relations/lazybtpredstarproper_8.ma".
16 include "basic_2/reduction/fpb.ma".
17 include "basic_2/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-.