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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/computation/cpxs_lift.ma".
16 include "basic_2/computation/fpbs.ma".
18 (* "QRST" PARALLEL COMPUTATION FOR CLOSURES *********************************)
20 (* Advanced properties ******************************************************)
22 lemma lstas_fpbs: ∀h,o,G,L,T1,T2,d2. ⦃G, L⦄ ⊢ T1 •*[h, d2] T2 →
23 ∀d1. d2 ≤ d1 → ⦃G, L⦄ ⊢ T1 ▪[h, o] d1 → ⦃G, L, T1⦄ ≥[h, o] ⦃G, L, T2⦄.
24 /3 width=5 by cpxs_fpbs, lstas_cpxs/ qed.
26 lemma sta_fpbs: ∀h,o,G,L,T,U,d.
27 ⦃G, L⦄ ⊢ T ▪[h, o] d+1 → ⦃G, L⦄ ⊢ T •*[h, 1] U →
28 ⦃G, L, T⦄ ≥[h, o] ⦃G, L, U⦄.
29 /2 width=5 by lstas_fpbs/ qed.
31 (* Note: this is used in the closure proof *)
32 lemma cpr_lpr_sta_fpbs: ∀h,o,G,L1,L2,T1,T2,U2,d2.
33 ⦃G, L1⦄ ⊢ T1 ➡ T2 → ⦃G, L1⦄ ⊢ ➡ L2 →
34 ⦃G, L2⦄ ⊢ T2 ▪[h, o] d2+1 → ⦃G, L2⦄ ⊢ T2 •*[h, 1] U2 →
35 ⦃G, L1, T1⦄ ≥[h, o] ⦃G, L2, U2⦄.
36 /4 width=5 by fpbs_strap1, cpr_lpr_fpbs, sta_cpx, fpbq_cpx/ qed.