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15 include "basic_2/computation/ltprs.ma".
16 include "basic_2/dynamic/lsubsv.ma".
18 (* "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **********************)
20 axiom yprs: ∀h. sd h → bi_relation lenv term.
22 interpretation "'big tree' parallel computation (closure)"
23 'BTPRedStar h g L1 T1 L2 T2 = (yprs h g L1 T1 L2 T2).
25 axiom cprs_yprs: ∀h,g,L,T1,T2. L ⊢ T1 ➡* T2 → h ⊢ ⦃L, T1⦄ ≥[g] ⦃L, T2⦄.
27 axiom sstas_yprs: ∀h,g,L,T1,T2. ⦃h, L⦄ ⊢ T1 •*[g] T2 →
28 h ⊢ ⦃L, T1⦄ ≥[g] ⦃L, T2⦄.
30 axiom lsubsv_yprs: ∀h,g,L1,L2,T. h ⊢ L2 ¡⊑[g] L1 → h ⊢ ⦃L1, T⦄ ≥[g] ⦃L2, T⦄.
32 axiom ltpr_cprs_yprs: ∀h,g,L1,L2,T1,T2. L1 ➡ L2 → L2 ⊢ T1 ➡* T2 →
33 h ⊢ ⦃L1, T1⦄ ≥[g] ⦃L2, T2⦄.
35 axiom ygt: ∀h. sd h → bi_relation lenv term.
37 interpretation "'big tree' proper parallel computation (closure)"
38 'BTPRedStarProper h g L1 T1 L2 T2 = (ygt h g L1 T1 L2 T2).
40 axiom fw_ygt: ∀h,g,L1,L2,T1,T2. ♯{L2, T2} < ♯{L1, T1} → h ⊢ ⦃L1, T1⦄ >[g] ⦃L2, T2⦄.
42 axiom ygt_yprs_trans: ∀h,g,L1,L,L2,T1,T,T2. h ⊢ ⦃L1, T1⦄ >[g] ⦃L, T⦄ →
43 h ⊢ ⦃L, T⦄ ≥[g] ⦃L2, T2⦄ → h ⊢ ⦃L1, T1⦄ >[g] ⦃L2, T2⦄.