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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/unfold/lsstas_lift.ma".
16 include "basic_2/reduction/fpb_lift.ma".
17 include "basic_2/computation/fpbs.ma".
19 (* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
21 (* Advanced properties ******************************************************)
23 lemma ssta_fpbs: ∀h,g,G,L,T,U,l.
24 ⦃G, L⦄ ⊢ T ▪[h, g] l+1 → ⦃G, L⦄ ⊢ T •[h, g] U →
25 ⦃G, L, T⦄ ≥[h, g] ⦃G, L, U⦄.
26 /3 width=2 by fpb_fpbs, ssta_fpb/ qed.
28 lemma lsstas_fpbs: ∀h,g,G,L,T1,T2,l2. ⦃G, L⦄ ⊢ T1 •*[h, g, l2] T2 →
29 ∀l1. l2 ≤ l1 → ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 → ⦃G, L, T1⦄ ≥[h, g] ⦃G, L, T2⦄.
30 #h #g #G #L #T1 #T2 #l2 #H @(lsstas_ind_dx … H) -l2 -T2 //
31 #l2 #T #T2 #HT1 #HT2 #IHT1 #l1 >commutative_plus #Hl21 #Hl1
32 elim (le_inv_plus_l … Hl21) -Hl21 #Hl12 #Hl21
33 lapply (lsstas_da_conf … HT1 … Hl1) -HT1
34 >(plus_minus_m_m … Hl12) -Hl12
35 /3 width=5 by ssta_fpb, fpbs_strap1/