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15 include "basic_2/substitution/lleq_fqus.ma".
16 include "basic_2/substitution/lleq_lleq.ma".
17 include "basic_2/computation/llpxs_lleq.ma".
18 include "basic_2/computation/fpbu.ma".
20 (* UNITARY "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **************)
22 (* Properties on lazy equivalence for local environments ********************)
24 lemma lleq_fpbu_trans: ∀h,g,F,K1,K2,T. K1 ⋕[T, 0] K2 →
25 ∀G,L2,U. ⦃F, K2, T⦄ ≻[h, g] ⦃G, L2, U⦄ →
26 ∃∃L1. ⦃F, K1, T⦄ ≻[h, g] ⦃G, L1, U⦄ & L1 ⋕[U, 0] L2.
27 #h #g #F #K1 #K2 #T #HT #G #L2 #U * -G -L2 -U
28 [ #G #L2 #U #H2 elim (lleq_fqup_trans … H2 … HT) -K2
29 /3 width=3 by fpbu_fqup, ex2_intro/
30 | /4 width=10 by fpbu_cpxs, cpxs_lleq_conf_sn, lleq_cpxs_trans, ex2_intro/
31 | /5 width=3 by fpbu_llpxs, lleq_llpxs_trans, lleq_canc_sn, ex2_intro/