matita/matita/contribs/lambdadelta/basic_2/syntax/tsts_tsts.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/tsts.ma".
  16
  17 (* SAME TOP TERM STRUCTURE **************************************************)
  18
  19 (* Main properties **********************************************************)
  20
  21 (* Basic_1: was: iso_trans *)
  22 theorem tsts_trans: ∀h,o. Transitive … (tsts h o).
  23 #h #o #T1 #T * -T1 -T
  24 [ #s1 #s #d #Hs1 #Hs #X #H
  25   elim (tsts_inv_sort1_deg … H … Hs) -s /2 width=3 by tsts_sort/
  26 | #i1 #i #H <(tsts_inv_lref1 … H) -H //
  27 | #l1 #l #H <(tsts_inv_gref1 … H) -H //
  28 | #I #V1 #V #T1 #T #X #H
  29   elim (tsts_inv_pair1 … H) -H #V2 #T2 #H destruct //
  30 ]
  31 qed-.
  32
  33 theorem tsts_canc_sn: ∀h,o. left_cancellable … (tsts h o).
  34 /3 width=3 by tsts_trans, tsts_sym/ qed-.
  35
  36 theorem tsts_canc_dx: ∀h,o. right_cancellable … (tsts h o).
  37 /3 width=3 by tsts_trans, tsts_sym/ qed-.