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4 (* ||A|| A project by Andrea Asperti *)
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15 include "basic_2/computation/fpbs_lift.ma".
17 (* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
19 (* Main properties **********************************************************)
21 theorem fpbs_trans: ∀h,g. tri_transitive … (fpbs h g).
22 /2 width=5 by tri_TC_transitive/ qed-.
24 (* Advanced properties ******************************************************)
26 lemma cpr_lpr_ssta_fpbs: ∀h,g,G,L1,L2,T1,T2,U2,l2.
27 ⦃G, L1⦄ ⊢ T1 ➡ T2 → ⦃G, L1⦄ ⊢ ➡ L2 →
28 ⦃G, L2⦄ ⊢ T2 ▪[h, g] l2+1 → ⦃G, L2⦄ ⊢ T2 •[h, g] U2 →
29 ⦃G, L1, T1⦄ ≥[h, g] ⦃G, L2, U2⦄.
30 /3 width=5 by fpbs_trans, cpr_lpr_fpbs, ssta_fpbs/ qed.