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

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  14
  15 include "basic_2/relocation/fqu_lleq.ma".
  16 include "basic_2/substitution/fqup.ma".
  17
  18 (* PLUS-ITERATED SUPCLOSURE *************************************************)
  19
  20 (* Properties on lazy equivalence for local environments ********************)
  21
  22 lemma lleq_fqup_trans: ∀G1,G2,L2,K2,T,U. ⦃G1, L2, T⦄ ⊃+ ⦃G2, K2, U⦄ →
  23                        ∀L1. L1 ⋕[0, T] L2 →
  24                        ∃∃K1. ⦃G1, L1, T⦄ ⊃+ ⦃G2, K1, U⦄ & K1 ⋕[0, U] K2.
  25 #G1 #G2 #L2 #K2 #T #U #H @(fqup_ind … H) -G2 -K2 -U
  26 [ #G2 #K2 #U #HTU #L1 #HL12 elim (lleq_fqu_trans … HTU … HL12) -L2
  27   /3 width=3 by fqu_fqup, ex2_intro/
  28 | #G #G2 #K #K2 #U #U2 #_ #HU2 #IHTU #L1 #HL12 elim (IHTU … HL12) -L2
  29   #K1 #HTU #HK1 elim (lleq_fqu_trans … HU2 … HK1) -K
  30   /3 width=5 by fqup_strap1, ex2_intro/
  31 ]
  32 qed-.