matita/matita/contribs/lambdadelta/basic_2/etc/lsubn/lsubn_lsubn.etc

   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/dynamic/lsubn_nta.ma".
  16
  17 (* LOCAL ENVIRONMENT REFINEMENT FOR NATIVE TYPE ASSIGNMENT ******************)
  18
  19 (* Main properties **********************************************************)
  20
  21 (* Note: new property *)
  22 theorem lsubn_trans: ∀h,L1,L. h ⊢ L1 :⊑ L → ∀L2. h ⊢ L :⊑ L2 → h ⊢ L1 :⊑ L2.
  23 #h #L1 #L #H elim H -L1 -L
  24 [ #X #H >(lsubn_inv_atom1 … H) -H //
  25 | #I #L1 #L #V #HL1 #H1W #IHL1 #X #H
  26   elim (lsubn_inv_pair1 … H) -H * #L2
  27   [ #HL2 #H #H2W destruct /4 width=1/
  28   | #W #H1VW #H2VW #HL2 #H1 #H2 destruct /3 width=3/
  29   ]
  30 | #L1 #L #V1 #W1 #H1VW1 #H2VW1 #HL1 #IHL1 #X #H
  31   elim (lsubn_inv_pair1 … H) -H * #L2
  32   [ #HL2 #H #HW destruct /3 width=1/
  33   | #V #_ #_ #_ #_ #H destruct
  34   ]
  35 ]
  36 qed.