matita/matita/contribs/lambdadelta/basic_2/syntax/ext2_ext2.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/ext2.ma".
  16
  17 (* EXTENSION TO BINDERS OF A RELATION FOR TERMS *****************************)
  18
  19 (* Main properties **********************************************************)
  20
  21 theorem ext2_trans: ∀R. Transitive … R → Transitive … (ext2 R).
  22 #R #HR #I1 #I #H elim H -I1 -I
  23 [ #I1 #J #H >(ext2_inv_unit_sn … H) -J /2 width=1 by ext2_unit/
  24 | #I1 #V1 #V #HV1 #J #H elim (ext2_inv_pair_sn … H) -H
  25   #V2 #HV2 #H destruct /3 width=3 by ext2_pair/
  26 ]
  27 qed-.