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15 include "basic_2/notation/relations/lazybtpredproper_8.ma".
16 include "basic_2/multiple/fleq.ma".
17 include "basic_2/reduction/fpbu.ma".
19 (* "QRST" PROPER PARALLEL REDUCTION FOR CLOSURES ****************************)
21 definition fpbc: ∀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⦄ ≡[0] ⦃G2, L2, T2⦄.
26 "'qrst' proper parallel reduction (closure)"
27 'LazyBTPRedProper h g G1 L1 T1 G2 L2 T2 = (fpbc h g G1 L1 T1 G2 L2 T2).
29 (* Baic properties **********************************************************)
31 lemma fpbu_fpbc: ∀h,g,G1,G2,L1,L2,T1,T2.
32 ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≻≡[h, g] ⦃G2, L2, T2⦄.
33 /2 width=5 by ex2_3_intro/ qed.