matita/matita/contribs/lambdadelta/basic_2/computation/fpbu_lleq.ma

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  14
  15 include "basic_2/substitution/lleq_fqus.ma".
  16 include "basic_2/substitution/lleq_lleq.ma".
  17 include "basic_2/computation/cpxs_lleq.ma".
  18 include "basic_2/computation/lpxs_lleq.ma".
  19 include "basic_2/computation/fpbu.ma".
  20
  21 (* UNITARY "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **************)
  22
  23 (* Properties on lazy equivalence for local environments ********************)
  24
  25 lemma lleq_fpbu_trans: ∀h,g,F,K1,K2,T. K1 ≡[T, 0] K2 →
  26                        ∀G,L2,U. ⦃F, K2, T⦄ ≻[h, g] ⦃G, L2, U⦄ →
  27                        ∃∃L1. ⦃F, K1, T⦄ ≻[h, g] ⦃G, L1, U⦄ & L1 ≡[U, 0] L2.
  28 #h #g #F #K1 #K2 #T #HT #G #L2 #U * -G -L2 -U
  29 [ #G #L2 #U #H2 elim (lleq_fqup_trans … H2 … HT) -K2
  30   /3 width=3 by fpbu_fqup, ex2_intro/
  31 | /4 width=10 by fpbu_cpxs, cpxs_lleq_conf_sn, lleq_cpxs_trans, ex2_intro/
  32 | #L2 #HKL2 #HnKL2 elim (lleq_lpxs_trans … HKL2 … HT) -HKL2
  33   /6 width=3 by fpbu_lpxs, lleq_canc_sn, ex2_intro/ (* 2 lleq_canc_sn *)
  34 ]
  35 qed-.