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15 include "basic_2/reduction/fpbc.ma".
16 include "basic_2/computation/fleq.ma".
17 include "basic_2/computation/fpbs_alt.ma".
19 (* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
21 (* Forward lemmas on equivalent "big tree" normal forms *********************)
23 lemma fpbs_fwd_fpb_sn: ∀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 ∃∃G,L,T. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G, L, T⦄ & ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄.
26 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim(fpbs_fpbsa … H) -H
27 #L #T #HT1 #HT2 #HL2 elim (eq_term_dec T1 T) #H destruct
28 [ -HT1 elim (fqus_inv_gen … HT2) -HT2
29 [ #HT2 elim (fqup_inv_step_sn … HT2) -HT2
30 /5 width=9 by fpbsa_inv_fpbs, fpbc_fqu, ex3_2_intro, ex2_3_intro, or_intror/
31 | * #HG #HL #HT destruct /3 width=1 by and3_intro, or_introl/
33 | elim (cpxs_neq_inv_step_sn … HT1 H) -HT1 -H
34 /5 width=9 by fpbsa_inv_fpbs, fpbc_cpx, ex3_2_intro, ex2_3_intro, or_intror/