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

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "basic_2/syntax/lveq_length.ma".
  16 include "basic_2/relocation/lifts_tdeq.ma".
  17 include "basic_2/static/lfxs_length.ma".
  18 include "basic_2/static/lfxs_fsle.ma".
  19 include "basic_2/static/lfdeq.ma".
  20
  21 (* DEGREE-BASED EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ******)
  22
  23 (* Advanved properties with free variables inclusion ************************)
  24
  25 lemma lfdeq_fsle_comp: ∀h,o. lfxs_fsle_compatible (cdeq h o).
  26 #h #o #L1 #L2 #T * #f1 #Hf1 #HL12
  27 lapply (frees_lfdeq_conf h o … Hf1 … HL12)
  28 lapply (lexs_fwd_length … HL12)
  29 /3 width=8 by lveq_length_eq, ex4_4_intro/ (**) (* full auto fails *)
  30 qed-.
  31
  32 (* Properties with length for local environments ****************************)
  33
  34 (* Basic_2A1: uses: lleq_lift_le lleq_lift_ge *)
  35 lemma lfdeq_lifts_bi: ∀L1,L2. |L1| = |L2| → ∀h,o,K1,K2,T. K1 ≛[h, o, T] K2 →
  36                       ∀b,f. ⬇*[b, f] L1 ≡ K1 → ⬇*[b, f] L2 ≡ K2 →
  37                       ∀U. ⬆*[f] T ≡ U → L1 ≛[h, o, U] L2.
  38 /3 width=9 by lfxs_lifts_bi, tdeq_lifts_sn/ qed-.
  39
  40 (* Forward lemmas with length for local environments ************************)
  41
  42 (* Basic_2A1: lleq_fwd_length *)
  43 lemma lfdeq_fwd_length: ∀h,o,L1,L2. ∀T:term. L1 ≛[h, o, T] L2 → |L1| = |L2|.
  44 /2 width=3 by lfxs_fwd_length/ qed-.
  45