matita/matita/contribs/lambdadelta/basic_2/substitution/fqus_lleq.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
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  14
  15 include "basic_2/substitution/fqup_lleq.ma".
  16 include "basic_2/substitution/fqus_alt.ma".
  17
  18 (* STAR-ITERATED SUPCLOSURE *************************************************)
  19
  20 (* Properties on lazy equivalence for local environments ********************)
  21
  22 lemma lleq_fqus_trans: ∀G1,G2,L2,K2,T,U. ⦃G1, L2, T⦄ ⊃* ⦃G2, K2, U⦄ →
  23                        ∀L1. L1 ⋕[T, 0] L2 →
  24                        ∃∃K1. ⦃G1, L1, T⦄ ⊃* ⦃G2, K1, U⦄ & K1 ⋕[U, 0] K2.
  25 #G1 #G2 #L2 #K2 #T #U #H #L1 #HL12 elim(fqus_inv_gen … H) -H
  26 [ #H elim (lleq_fqup_trans … H … HL12) -L2 /3 width=3 by fqup_fqus, ex2_intro/
  27 | * #HG #HL #HT destruct /2 width=3 by ex2_intro/
  28 ]
  29 qed-.