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4 (* ||A|| A project by Andrea Asperti *)
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15 include "basic_2/unfold/lsstas_lift.ma".
16 include "basic_2/dynamic/ygt.ma".
18 (* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
20 (* Advanced properties ******************************************************)
22 lemma lsstas_ygt: ∀h,g,G,L,T1,T2,l2. ⦃G, L⦄ ⊢ T1 •*[h, g, l2] T2 → (T1 = T2 → ⊥) →
23 ∀l1. l2 ≤ l1 → ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 → ⦃G, L, T1⦄ >[h, g] ⦃G, L, T2⦄.
24 #h #g #G #L #T1 #T2 #l2 #H @(lsstas_ind_dx … H) -l2 -T2
26 | #l2 #T #T2 #HT1 #HT2 #IHT1 #HT12 #l1 #Hl21
27 elim (term_eq_dec T1 T) #H destruct [ -IHT1 |]
28 [ elim (le_inv_plus_l … Hl21) -Hl21 #_ #Hl1
29 >(plus_minus_m_m … Hl1) -Hl1 /3 width=5 by ysc_ssta, ygt_inj/
30 | #Hl1 >commutative_plus in Hl21; #Hl21
31 elim (le_inv_plus_l … Hl21) -Hl21 #Hl12 #Hl21
32 lapply (lsstas_da_conf … HT1 … Hl1) -HT1
33 >(plus_minus_m_m … Hl12) -Hl12
34 /4 width=5 by ypr_ssta, ygt_strap1/