include "basic_2/substitution/lleq_fqus.ma".
include "basic_2/substitution/lleq_lleq.ma".
-include "basic_2/computation/llpxs_lleq.ma".
+include "basic_2/computation/cpxs_lleq.ma".
+include "basic_2/computation/lpxs_lleq.ma".
include "basic_2/computation/fpbu.ma".
(* UNITARY "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **************)
(* Properties on lazy equivalence for local environments ********************)
-lemma lleq_fpbu_trans: â\88\80h,g,F,K1,K2,T. K1 â\8b\95[T, 0] K2 →
+lemma lleq_fpbu_trans: â\88\80h,g,F,K1,K2,T. K1 â\89¡[T, 0] K2 →
∀G,L2,U. ⦃F, K2, T⦄ ≻[h, g] ⦃G, L2, U⦄ →
- â\88\83â\88\83L1. â¦\83F, K1, Tâ¦\84 â\89»[h, g] â¦\83G, L1, Uâ¦\84 & L1 â\8b\95[U, 0] L2.
+ â\88\83â\88\83L1. â¦\83F, K1, Tâ¦\84 â\89»[h, g] â¦\83G, L1, Uâ¦\84 & L1 â\89¡[U, 0] L2.
#h #g #F #K1 #K2 #T #HT #G #L2 #U * -G -L2 -U
[ #G #L2 #U #H2 elim (lleq_fqup_trans … H2 … HT) -K2
/3 width=3 by fpbu_fqup, ex2_intro/
-| /4 width=10 by fpbu_cpxs, lleq_cpxs_conf_sn, lleq_cpxs_trans, ex2_intro/
-| /5 width=3 by fpbu_llpxs, lleq_llpxs_trans, lleq_canc_sn, ex2_intro/
+| /4 width=10 by fpbu_cpxs, cpxs_lleq_conf_sn, lleq_cpxs_trans, ex2_intro/
+| #L2 #HKL2 #HnKL2 elim (lleq_lpxs_trans … HKL2 … HT) -HKL2
+ /6 width=3 by fpbu_lpxs, lleq_canc_sn, ex2_intro/ (* 2 lleq_canc_sn *)
]
qed-.