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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "basic_2/static/lfdeq_fqus.ma".
16 include "basic_2/rt_transition/cpx_lfdeq.ma".
17 include "basic_2/rt_transition/lfpx_lfdeq.ma".
18 include "basic_2/rt_transition/fpb.ma".
20 (* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
22 (* Properties with degree-based equivalence for local environments **********)
24 (* Basic_2A1: was just: lleq_fpb_trans *)
25 lemma lfdeq_fpb_trans: ∀h,o,F,K1,K2,T. K1 ≡[h, o, T] K2 →
26 ∀G,L2,U. ⦃F, K2, T⦄ ≻[h, o] ⦃G, L2, U⦄ →
27 ∃∃L1,U0. ⦃F, K1, T⦄ ≻[h, o] ⦃G, L1, U0⦄ & U0 ≡[h, o] U & L1 ≡[h, o, U] L2.
28 #h #o #F #K1 #K2 #T #HT #G #L2 #U * -G -L2 -U
29 [ #G #L2 #U #H2 elim (lfdeq_fqu_trans … H2 … HT) -K2
30 /3 width=5 by fpb_fqu, ex3_2_intro/
31 | #U #HTU #HnTU elim (lfdeq_cpx_trans … HT … HTU) -HTU
32 /5 width=10 by fpb_cpx, cpx_lfdeq_conf_sn, tdeq_trans, tdeq_lfdeq_conf_sn, ex3_2_intro/
33 | #L2 #HKL2 #HnKL2 elim (lfdeq_lfpx_trans … HKL2 … HT) -HKL2
34 /6 width=5 by fpb_lfpx, lfdeq_canc_sn, ex3_2_intro/ (* 2 lleq_canc_sn *)