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

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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   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/static/lfxs_fqup.ma".
  16 include "basic_2/static/lfdeq.ma".
  17
  18 (* DEGREE-BASED EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ******)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 lemma lfdeq_refl: ∀h,o,T. reflexive … (lfdeq h o T).
  23 /2 width=1 by lfxs_refl/ qed.
  24
  25 lemma lfdeq_pair_refl: ∀h,o,V1,V2. V1 ≛[h, o] V2 →
  26                        ∀I,L. ∀T:term. L.ⓑ{I}V1 ≛[h, o, T] L.ⓑ{I}V2.
  27 /2 width=1 by lfxs_pair_refl/ qed.
  28
  29 (* Advanced inversion lemmas ************************************************)
  30
  31 lemma lfdeq_inv_bind_void: ∀h,o,p,I,L1,L2,V,T. L1 ≛[h, o, ⓑ{p,I}V.T] L2 →
  32                            L1 ≛[h, o, V] L2 ∧ L1.ⓧ ≛[h, o, T] L2.ⓧ.
  33 /2 width=3 by lfxs_inv_bind_void/ qed-.
  34
  35 (* Advanced forward lemmas **************************************************)
  36
  37 lemma lfdeq_fwd_bind_dx_void: ∀h,o,p,I,L1,L2,V,T.
  38                               L1 ≛[h, o, ⓑ{p,I}V.T] L2 → L1.ⓧ ≛[h, o, T] L2.ⓧ.
  39 /2 width=4 by lfxs_fwd_bind_dx_void/ qed-.