matita/matita/contribs/lambdadelta/basic_2/static/lfeq_fsle.ma

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  14
  15 include "basic_2/static/lfxs_length.ma".
  16 include "basic_2/static/lfxs_fsle.ma".
  17 include "basic_2/static/lfeq.ma".
  18
  19 (* SYNTACTIC EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES *********)
  20
  21 (* Properties with free variables inclusion for restricted closures *********)
  22
  23 lemma lfeq_fsle_comp: lfxs_fsle_compatible ceq.
  24 #L1 #L2 #T #HL12
  25 elim (frees_total L1 T)
  26 /4 width=8 by frees_lfeq_conf, lfxs_fwd_length, lveq_length_eq, sle_refl, ex4_4_intro/
  27 qed.
  28
  29 (* Forward lemmas with free variables inclusion for restricted closures *****)
  30
  31 lemma lfeq_lfxs_trans: ∀R. lfeq_transitive R →
  32                        ∀L1,L,T. L1 ≡[T] L → ∀L2. L ⪤*[R, T] L2 → L1 ⪤*[R, T] L2.
  33 /4 width=16 by lfeq_fsle_comp, lfxs_trans_fsle, lfxs_trans_next/ qed-.