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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/static/ssta_ssta.ma".
16 include "basic_2/computation/cpxs_lift.ma".
17 include "basic_2/computation/fpbu.ma".
19 (* UNITARY "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **************)
21 (* Advanced properties ******************************************************)
23 lemma lsstas_fpbu: ∀h,g,G,L,T1,T2,l2. ⦃G, L⦄ ⊢ T1 •*[h, g, l2] T2 → (T1 = T2 → ⊥) →
24 ∀l1. l2 ≤ l1 → ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 → ⦃G, L, T1⦄ ≻[h, g] ⦃G, L, T2⦄.
25 /4 width=5 by fpbu_cpxs, lsstas_cpxs/ qed.
27 lemma ssta_fpbu: ∀h,g,G,L,T1,T2,l. ⦃G, L⦄ ⊢ T1 ▪[h, g] l+1 →
28 ⦃G, L⦄ ⊢ T1 •[h, g] T2 → ⦃G, L, T1⦄ ≻[h, g] ⦃G, L, T2⦄.
29 #h #g #G #L #T1 #T2 #l #HT1 #HT12 elim (eq_term_dec T1 T2)
30 /3 width=5 by ssta_lsstas, lsstas_fpbu/ #H destruct
31 elim (ssta_inv_refl_pos … HT1 … HT12)