matita/matita/contribs/lambdadelta/static_2/static/lsubr_lsubr.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/static/lsubr.ma".
  16
  17 (* RESTRICTED REFINEMENT FOR LOCAL ENVIRONMENTS *****************************)
  18
  19 (* Main properties **********************************************************)
  20
  21 theorem lsubr_trans: Transitive … lsubr.
  22 #L1 #L #H elim H -L1 -L //
  23 [ #I #L1 #L #_ #IH #X #H elim (lsubr_inv_bind1 … H) -H *
  24   [ #L2 #HL2 #H | #L2 #V #W #HL2 #H1 #H2 | #I1 #I2 #L2 #V #Hl2 #H1 #H2 ]
  25   destruct /3 width=1 by lsubr_bind, lsubr_beta, lsubr_unit/
  26 | #L1 #L #V #W #_ #IH #X #H elim (lsubr_inv_abst1 … H) -H *
  27   [ #L2 #HL2 #H | #I #L2 #HL2 #H ]
  28   destruct /3 width=1 by lsubr_beta, lsubr_unit/
  29 | #I1 #I2 #L1 #L #V #_ #IH #X #H elim (lsubr_inv_unit1 … H) -H
  30   /4 width=1 by lsubr_unit/
  31 ]
  32 qed-.