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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "basic_2/computation/fpbs_alt.ma".
16 include "basic_2/computation/fpbg.ma".
18 (* GENERAL "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **************)
20 (* Advanced forward lemmas **************************************************)
22 lemma fpbg_fwd_fpbs: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄ →
23 ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
24 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G2 -L2 -T2
25 /3 width=5 by cpxs_fqup_fpbs, fpbs_trans, lpxs_fpbs, cpxs_fpbs/
28 lemma fpbg_fwd_fpb_sn: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄ →
29 ∃∃G,L,T. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G, L, T⦄ & ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄.
30 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G2 -L2 -T2
31 [ #L2 #T2 #HT12 #H #HL12
32 elim (cpxs_neq_inv_step_sn … HT12 H) -HT12 -H
33 /4 width=9 by fpbsa_inv_fpbs, fpbc_cpx, ex3_2_intro, ex2_3_intro/
34 | #G2 #L #L2 #T #T2 #HT1 #HT2 #HL2 elim (eq_term_dec T1 T) #H destruct
35 [ -HT1 elim (fqup_inv_step_sn … HT2) -HT2
36 /4 width=9 by fpbsa_inv_fpbs, fpbc_fqu, ex3_2_intro, ex2_3_intro/
37 | elim (cpxs_neq_inv_step_sn … HT1 H) -HT1 -H
38 /5 width=9 by fpbsa_inv_fpbs, fpbc_cpx, fqup_fqus, ex3_2_intro, ex2_3_intro/
43 (* Advanced properties ******************************************************)
45 lemma fqu_fpbs_fpbg: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G, L, T⦄ →
46 ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄.
47 #h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H elim(fpbs_fpbsa … H) -H
48 #L0 #T0 #HT0 #HT02 #HL02 elim (fqu_cpxs_trans … HT0 … H1) -T
49 /3 width=7 by fpbg_fqup, fqus_strap2_fqu/