matita/matita/contribs/lambdadelta/basic_2A/reduction/fpb_lleq.ma

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  14
  15 include "basic_2A/multiple/lleq_fqus.ma".
  16 include "basic_2A/multiple/lleq_lleq.ma".
  17 include "basic_2A/reduction/lpx_lleq.ma".
  18 include "basic_2A/reduction/fpb.ma".
  19
  20 (* "RST" PROPER PARALLEL COMPUTATION FOR CLOSURES ***************************)
  21
  22 (* Properties on lazy equivalence for local environments ********************)
  23
  24 lemma lleq_fpb_trans: ∀h,g,F,K1,K2,T. K1 ≡[T, 0] K2 →
  25                       ∀G,L2,U. ⦃F, K2, T⦄ ≻[h, g] ⦃G, L2, U⦄ →
  26                       ∃∃L1. ⦃F, K1, T⦄ ≻[h, g] ⦃G, L1, U⦄ & L1 ≡[U, 0] L2.
  27 #h #g #F #K1 #K2 #T #HT #G #L2 #U * -G -L2 -U
  28 [ #G #L2 #U #H2 elim (lleq_fqu_trans … H2 … HT) -K2
  29   /3 width=3 by fpb_fqu, ex2_intro/
  30 | /4 width=10 by fpb_cpx, cpx_lleq_conf_sn, lleq_cpx_trans, ex2_intro/
  31 | #L2 #HKL2 #HnKL2 elim (lleq_lpx_trans … HKL2 … HT) -HKL2
  32   /6 width=3 by fpb_lpx, lleq_canc_sn, ex2_intro/ (* 2 lleq_canc_sn *)
  33 ]
  34 qed-.