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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 "static_2/static/reqx_fqus.ma".
16 include "basic_2/rt_transition/cpx_reqx.ma".
17 include "basic_2/rt_transition/lpx_reqx.ma".
18 include "basic_2/rt_transition/fpb.ma".
20 (* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
22 (* Properties with sort-irrelevant equivalence for local environments *******)
24 lemma teqx_fpb_trans: ∀h,U2,U1. U2 ≛ U1 →
25 ∀G1,G2,L1,L2,T1. ⦃G1,L1,U1⦄ ≻[h] ⦃G2,L2,T1⦄ →
26 ∃∃L,T2. ⦃G1,L1,U2⦄ ≻[h] ⦃G2,L,T2⦄ & T2 ≛ T1 & L ≛[T1] L2.
27 #h #U2 #U1 #HU21 #G1 #G2 #L1 #L2 #T1 * -G2 -L2 -T1
29 elim (teqx_fqu_trans … H … HU21) -H
30 /3 width=5 by fpb_fqu, ex3_2_intro/
32 elim (teqx_cpx_trans … HU21 … HUT1) -HUT1
33 /6 width=5 by fpb_cpx, teqx_canc_sn, teqx_trans, ex3_2_intro/
34 | /6 width=5 by fpb_lpx, rpx_teqx_div, teqx_reqx_conf, ex3_2_intro/
38 (* Basic_2A1: was just: lleq_fpb_trans *)
39 lemma reqx_fpb_trans: ∀h,F,K1,K2,T. K1 ≛[T] K2 →
40 ∀G,L2,U. ⦃F,K2,T⦄ ≻[h] ⦃G,L2,U⦄ →
41 ∃∃L1,U0. ⦃F,K1,T⦄ ≻[h] ⦃G,L1,U0⦄ & U0 ≛ U & L1 ≛[U] L2.
42 #h #F #K1 #K2 #T #HT #G #L2 #U * -G -L2 -U
43 [ #G #L2 #U #H2 elim (reqx_fqu_trans … H2 … HT) -K2
44 /3 width=5 by fpb_fqu, ex3_2_intro/
45 | #U #HTU #HnTU elim (reqx_cpx_trans … HT … HTU) -HTU
46 /5 width=11 by fpb_cpx, cpx_reqx_conf_sn, teqx_trans, teqx_reqx_conf, ex3_2_intro/ (**) (* time: 36s on dev *)
47 | #L2 #HKL2 #HnKL2 elim (reqx_lpx_trans … HKL2 … HT) -HKL2
48 /6 width=5 by fpb_lpx, (* 2x *) reqx_canc_sn, ex3_2_intro/