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/computation/lpxs_lpxs.ma".
16 include "basic_2/computation/fpbs_alt.ma".
17 include "basic_2/computation/fpbg.ma".
19 (* GENERAL "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **************)
21 (* Advanced forward lemmas **************************************************)
23 lemma fpbg_fwd_fpbs: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄ →
24 ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
25 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G2 -L2 -T2
26 /3 width=5 by cpxs_fqus_lpxs_fpbs, cpxs_fqup_fpbs, fpbs_trans, lpxs_fpbs, cpxs_fpbs/
29 lemma fpbg_fwd_fpbc_sn: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄ →
30 ∃∃G,L,T. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G, L, T⦄ & ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄.
31 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G2 -L2 -T2
32 [ /4 width=5 by fpbc_cpxs, lpxs_fpbs, ex2_3_intro/
33 | #G2 #L #L2 #T #T2 #HT1 #HT2 #HL2 elim (eq_term_dec T1 T) #H destruct
34 [ -HT1 /3 width=5 by fpbc_fqup, lpxs_fpbs, ex2_3_intro/
35 | /5 width=9 by fpbc_cpxs, fpbsa_inv_fpbs, fqup_fqus, ex3_2_intro, ex2_3_intro/
37 | #G2 #L #L0 #L2 #T #T2 #HT1 #HT2 #HL0 #H0 #HL02 #H02
38 lapply (lpxs_trans … HL0 … HL02) #HL2
39 elim (eq_term_dec T1 T) #H destruct
40 [ -HT1 elim (fqus_inv_gen … HT2) -HT2
41 [ /3 width=5 by fpbc_fqup, lpxs_fpbs, ex2_3_intro/
42 | * #H1 #H2 #H3 destruct
43 /4 width=5 by fpbc_lpxs, lpxs_fpbs, ex2_3_intro/
45 | /4 width=9 by fpbc_cpxs, fpbsa_inv_fpbs, ex3_2_intro, ex2_3_intro/
50 (* Advanced properties ******************************************************)
52 lemma fqu_fpbs_fpbg: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G, L, T⦄ →
53 ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄.
54 #h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H elim(fpbs_fpbsa … H) -H
55 #L0 #T0 #HT0 #HT02 #HL02 elim (fqu_cpxs_trans … HT0 … H1) -T
56 /3 width=7 by fpbg_fqup, fqus_strap2_fqu/