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15 include "basic_2/notation/relations/btpredstaralt_8.ma".
16 include "basic_2/computation/fpbs_fpbs.ma".
18 (* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
20 (* Note: alternative definition of fpbs *)
21 definition fpbsa: ∀h. sd h → tri_relation genv lenv term ≝
22 λh,g,G1,L1,T1,G2,L2,T2.
23 ∃∃L,T. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L, T⦄ & ⦃G2, L⦄ ⊢ T ➡*[h, g] T2 & ⦃G2, L⦄ ⊢ ➡*[h, g] L2.
25 interpretation "'big tree' parallel computation (closure) alternative"
26 'BTPRedStarAlt h g G1 L1 T1 G2 L2 T2 = (fpbsa h g G1 L1 T1 G2 L2 T2).
28 (* Main inversion lemmas ****************************************************)
30 theorem fpbsa_inv_fpbs: ∀h,g,G1,G2,L1,L2,T1,T2.
31 ⦃G1, L1, T1⦄ ≥≥[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
32 #h #g #G1 #G2 #L1 #L2 #T1 #T2 *
33 /4 width=5 by fpbs_trans, fsups_fpbs, cpxs_fpbs, lpxs_fpbs/