(* Properties with degree-based equivalence for local environments **********)
(* Basic_2A1: was just: lleq_fpb_trans *)
-lemma lfdeq_fpb_trans: â\88\80h,o,F,K1,K2,T. K1 â\89¡[h, o, T] K2 →
+lemma lfdeq_fpb_trans: â\88\80h,o,F,K1,K2,T. K1 â\89\9b[h, o, T] K2 →
∀G,L2,U. ⦃F, K2, T⦄ ≻[h, o] ⦃G, L2, U⦄ →
- â\88\83â\88\83L1,U0. â¦\83F, K1, Tâ¦\84 â\89»[h, o] â¦\83G, L1, U0â¦\84 & U0 â\89¡[h, o] U & L1 â\89¡[h, o, U] L2.
+ â\88\83â\88\83L1,U0. â¦\83F, K1, Tâ¦\84 â\89»[h, o] â¦\83G, L1, U0â¦\84 & U0 â\89\9b[h, o] U & L1 â\89\9b[h, o, U] L2.
#h #o #F #K1 #K2 #T #HT #G #L2 #U * -G -L2 -U
[ #G #L2 #U #H2 elim (lfdeq_fqu_trans … H2 … HT) -K2
/3 width=5 by fpb_fqu, ex3_2_intro/
| #U #HTU #HnTU elim (lfdeq_cpx_trans … HT … HTU) -HTU
- /5 width=10 by fpb_cpx, cpx_lfdeq_conf_sn, tdeq_trans, tdeq_lfdeq_conf_sn, ex3_2_intro/
+ /5 width=10 by fpb_cpx, cpx_lfdeq_conf_sn, tdeq_trans, tdeq_lfdeq_conf, ex3_2_intro/
| #L2 #HKL2 #HnKL2 elim (lfdeq_lfpx_trans … HKL2 … HT) -HKL2
- /6 width=5 by fpb_lfpx, lfdeq_canc_sn, ex3_2_intro/ (* 2 lleq_canc_sn *)
+ /6 width=5 by fpb_lfpx, (* 2x *) lfdeq_canc_sn, ex3_2_intro/
]
qed-.