matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_reqx.ma

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  14
  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".
  19
  20 (* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
  21
  22 (* Properties with sort-irrelevant equivalence for local environments *******)
  23
  24 lemma teqx_fpb_trans:
  25       ∀U2,U1. U2 ≛ U1 →
  26       ∀G1,G2,L1,L2,T1. ❪G1,L1,U1❫ ≻ ❪G2,L2,T1❫ →
  27       ∃∃L,T2. ❪G1,L1,U2❫ ≻ ❪G2,L,T2❫ & T2 ≛ T1 & L ≛[T1] L2.
  28 #U2 #U1 #HU21 #G1 #G2 #L1 #L2 #T1 * -G2 -L2 -T1
  29 [ #G2 #L2 #T1 #H
  30   elim (teqx_fqu_trans … H … HU21) -H
  31   /3 width=5 by fpb_fqu, ex3_2_intro/
  32 | #T1 #HUT1 #HnUT1
  33   elim (teqx_cpx_trans … HU21 … HUT1) -HUT1
  34   /6 width=5 by fpb_cpx, teqx_canc_sn, teqx_trans, ex3_2_intro/
  35 | /6 width=5 by fpb_lpx, rpx_teqx_div, teqx_reqx_conf, ex3_2_intro/
  36 ]
  37 qed-.
  38
  39 (* Basic_2A1: was just: lleq_fpb_trans *)
  40 lemma reqx_fpb_trans:
  41       ∀F,K1,K2,T. K1 ≛[T] K2 →
  42       ∀G,L2,U. ❪F,K2,T❫ ≻ ❪G,L2,U❫ →
  43       ∃∃L1,U0. ❪F,K1,T❫ ≻ ❪G,L1,U0❫ & U0 ≛ U & L1 ≛[U] L2.
  44 #F #K1 #K2 #T #HT #G #L2 #U * -G -L2 -U
  45 [ #G #L2 #U #H2 elim (reqx_fqu_trans … H2 … HT) -K2
  46   /3 width=5 by fpb_fqu, ex3_2_intro/
  47 | #U #HTU #HnTU elim (reqx_cpx_trans … HT … HTU) -HTU
  48   /5 width=11 by fpb_cpx, cpx_reqx_conf_sn, teqx_trans, teqx_reqx_conf, ex3_2_intro/ (**) (* time: 36s on dev *)
  49 | #L2 #HKL2 #HnKL2 elim (reqx_lpx_trans … HKL2 … HT) -HKL2
  50   /6 width=5 by fpb_lpx, (* 2x *) reqx_canc_sn, ex3_2_intro/
  51 ]
  52 qed-.