matita/matita/contribs/lambdadelta/basic_2A/static/lsubd_lsubd.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_2A/static/lsubd_da.ma".
  16
  17 (* LOCAL ENVIRONMENT REFINEMENT FOR DEGREE ASSIGNMENT ***********************)
  18
  19 (* Main properties **********************************************************)
  20
  21 theorem lsubd_trans: ∀h,g,G. Transitive … (lsubd h g G).
  22 #h #g #G #L1 #L #H elim H -L1 -L
  23 [ #X #H >(lsubd_inv_atom1 … H) -H //
  24 | #I #L1 #L #Y #HL1 #IHL1 #X #H
  25   elim (lsubd_inv_pair1 … H) -H * #L2
  26   [ #HL2 #H destruct /3 width=1 by lsubd_pair/
  27   | #W #V #d #HV #HW #HL2 #H1 #H2 #H3 destruct
  28     /3 width=3 by lsubd_beta, lsubd_da_trans/
  29   ]
  30 | #L1 #L #W #V #d #HV #HW #HL1 #IHL1 #X #H
  31   elim (lsubd_inv_pair1 … H) -H * #L2
  32   [ #HL2 #H destruct /3 width=5 by lsubd_beta, lsubd_da_conf/
  33   | #W0 #V0 #d0 #_ #_ #_ #H destruct
  34   ]
  35 ]
  36 qed-.