matita/matita/contribs/lambdadelta/static_2/syntax/acle_acle.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/acle.ma".
  16
  17 (* APPLICABILITY CONDITION PREORDER *****************************************)
  18
  19 (* Main properties **********************************************************)
  20
  21 theorem acle_trans: Transitive … acle.
  22 #a1 #a #Ha1 #a2 #Ha2 #m1 #Hm1
  23 elim (Ha1 … Hm1) -Ha1 -Hm1 #m #Ha #Hm1
  24 elim (Ha2 … Ha) -Ha2 -Ha #m2 #Ha2 #Hm2
  25 /3 width=5 by transitive_le, ex2_intro/
  26 qed-.