matita/matita/contribs/lambdadelta/basic_2/etc/fid/lfeq_fid.etc

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
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   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "basic_2/relocation/lexs_length.ma".
  16 include "basic_2/static/frees_fqup.ma".
  17 include "basic_2/static/fid.ma".
  18 include "basic_2/static/lfeq.ma".
  19
  20 (* SYNTACTIC EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES *********)
  21
  22 (* properties with free variables identity for restricted closures **********)
  23
  24 lemma fid_lfeq: ∀L1,L2. |L1| = |L2| → ∀T. 𝐈⦃L1, T⦄ → L1 ≡[T] L2.
  25 #L1 #L2 #HL1 #T #HT
  26 elim (frees_total L1 T) #f #Hf
  27 /4 width=3 by lexs_length_isid, ex2_intro/
  28 qed.
  29
  30 (* Advanced properties with free variables identity for restricted closures *)
  31
  32 lemma fid_length: ∀L1,L2. |L1| = |L2| → ∀T. 𝐈⦃L1, T⦄ → 𝐈⦃L2, T⦄.
  33 #L1 #L2 #HL #T #HT #g #Hg
  34 elim (frees_total L1 T) #f #Hf
  35 lapply (frees_mono f … Hg) -Hg
  36 [ /3 width=4 by fid_lfeq, frees_lfeq_conf/
  37 | /3 width=3 by isid_eq_repl_back/
  38 ]
  39 qed-.