1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "basic_2/unfold/lsstas_lift.ma".
16 include "basic_2/reduction/fpb_lift.ma".
17 include "basic_2/reduction/fpbc_lift.ma".
18 include "basic_2/computation/fpbg.ma".
20 (* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
22 (* Advanced properties ******************************************************)
24 lemma lsstas_fpbg: ∀h,g,G,L,T1,T2,l2. ⦃G, L⦄ ⊢ T1 •*[h, g, l2] T2 → (T1 = T2 → ⊥) →
25 ∀l1. l2 ≤ l1 → ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 → ⦃G, L, T1⦄ >[h, g] ⦃G, L, T2⦄.
26 #h #g #G #L #T1 #T2 #l2 #H @(lsstas_ind_dx … H) -l2 -T2
28 | #l2 #T #T2 #HT1 #HT2 #IHT1 #HT12 #l1 #Hl21
29 elim (term_eq_dec T1 T) #H destruct [ -IHT1 |]
30 [ elim (le_inv_plus_l … Hl21) -Hl21 #_ #Hl1
31 >(plus_minus_m_m … Hl1) -Hl1 /3 width=5 by ssta_fpbc, fpbg_inj/
32 | #Hl1 >commutative_plus in Hl21; #Hl21
33 elim (le_inv_plus_l … Hl21) -Hl21 #Hl12 #Hl21
34 lapply (lsstas_da_conf … HT1 … Hl1) -HT1
35 >(plus_minus_m_m … Hl12) -Hl12
36 /4 width=5 by ssta_fpb, fpbg_strap1/