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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
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15 include "basic_2/reduction/fpb_lift.ma".
16 include "basic_2/computation/cpxs_lift.ma".
17 include "basic_2/computation/fpbs.ma".
19 (* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
21 (* Advanced properties ******************************************************)
23 lemma lsstas_fpbs: ∀h,g,G,L,T1,T2,l2. ⦃G, L⦄ ⊢ T1 •*[h, g, l2] T2 →
24 ∀l1. l2 ≤ l1 → ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 → ⦃G, L, T1⦄ ≥[h, g] ⦃G, L, T2⦄.
25 /3 width=5 by cpxs_fpbs, lsstas_cpxs/ qed.
27 lemma ssta_fpbs: ∀h,g,G,L,T,U,l.
28 ⦃G, L⦄ ⊢ T ▪[h, g] l+1 → ⦃G, L⦄ ⊢ T •[h, g] U →
29 ⦃G, L, T⦄ ≥[h, g] ⦃G, L, U⦄.
30 /4 width=2 by fpb_fpbs, ssta_fpb/ qed.
32 (* Note: this is used in the closure proof *)
33 lemma cpr_lpr_ssta_fpbs: ∀h,g,G,L1,L2,T1,T2,U2,l2.
34 ⦃G, L1⦄ ⊢ T1 ➡ T2 → ⦃G, L1⦄ ⊢ ➡ L2 →
35 ⦃G, L2⦄ ⊢ T2 ▪[h, g] l2+1 → ⦃G, L2⦄ ⊢ T2 •[h, g] U2 →
36 ⦃G, L1, T1⦄ ≥[h, g] ⦃G, L2, U2⦄.
37 /4 width=5 by fpbs_strap1, cpr_lpr_fpbs, ssta_cpx, fpb_cpx/ qed.