1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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11 (* v GNU General Public License Version 2 *)
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15 include "basic_2/computation/fpbg_fpbg.ma".
16 include "basic_2/computation/fpbr.ma".
18 (* RESTRICTED "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES ***********)
20 (* Advanced forward lemmas **************************************************)
22 lemma fpbr_fwd_fpbg: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃≥[h, g] ⦃G2, L2, T2⦄ →
23 ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄.
24 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim (fpbr_inv_fqu_fpbs … H) -H
25 /2 width=5 by fqu_fpbs_fpbg/
28 lemma fpbr_fwd_fpbs: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃≥[h, g] ⦃G2, L2, T2⦄ →
29 ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
30 /3 width=5 by fpbr_fwd_fpbg, fpbg_fwd_fpbs/
33 (* Main properties **********************************************************)
35 theorem fpbr_trans: ∀h,g. tri_transitive … (fpbr h g).
36 /3 width=5 by fpbr_fwd_fpbs, fpbr_fpbs_trans/ qed-.