matita/matita/contribs/lambdadelta/static_2/syntax/tueq_tueq.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 "static_2/syntax/tueq.ma".
  16
  17 (* TAIL SORT-IRRELEVANT EQUIVALENCE ON TERMS ********************************)
  18
  19 (* Main properties **********************************************************)
  20
  21 theorem tueq_trans: Transitive … tueq.
  22 #T1 #T #H elim H -T1 -T
  23 [ #s1 #s #X #H
  24   elim (tueq_inv_sort1 … H) -s /2 width=1 by tueq_sort/
  25 | #i1 #i #H //
  26 | #l1 #l #H //
  27 | #p #I #V #T1 #T #_ #IHT #X #H
  28   elim (tueq_inv_bind1 … H) -H /3 width=1 by tueq_bind/
  29 | #V #T1 #T #_ #IHT #X #H
  30   elim (tueq_inv_appl1 … H) -H /3 width=1 by tueq_appl/
  31 | #V1 #V #T1 #T #_ #_ #IHV #IHT #X #H
  32   elim (tueq_inv_cast1 … H) -H /3 width=1 by tueq_cast/
  33 ]
  34 qed-.
  35
  36 theorem tueq_canc_sn: left_cancellable … tueq.
  37 /3 width=3 by tueq_trans, tueq_sym/ qed-.
  38
  39 theorem tueq_canc_dx: right_cancellable … tueq.
  40 /3 width=3 by tueq_trans, tueq_sym/ qed-.
  41
  42 theorem tueq_repl: ∀T1,T2. T1 ≅ T2 →
  43                    ∀U1. T1 ≅ U1 → ∀U2. T2 ≅ U2 → U1 ≅ U2.
  44 /3 width=3 by tueq_canc_sn, tueq_trans/ qed-.