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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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15 include "basic_2/computation/cpxs_lift.ma".
16 include "basic_2/computation/fpbs.ma".
18 (* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
20 (* Advanced properties ******************************************************)
22 lemma lsstas_fpbs: ∀h,g,G,L,T1,T2,l2. ⦃G, L⦄ ⊢ T1 •*[h, g, l2] T2 →
23 ∀l1. l2 ≤ l1 → ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 → ⦃G, L, T1⦄ ≥[h, g] ⦃G, L, T2⦄.
24 /3 width=5 by cpxs_fpbs, lsstas_cpxs/ qed.
26 lemma ssta_fpbs: ∀h,g,G,L,T,U,l.
27 ⦃G, L⦄ ⊢ T ▪[h, g] l+1 → ⦃G, L⦄ ⊢ T •[h, g] U →
28 ⦃G, L, T⦄ ≥[h, g] ⦃G, L, U⦄.
29 /3 width=5 by lsstas_fpbs, ssta_lsstas/ qed.