matita/matita/contribs/lambda_delta/basic_2/static/lsubss_lsubss.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/static/lsubss_ssta.ma".
  16
  17 (* LOCAL ENVIRONMENT REFINEMENT FOR STATIC TYPE ASSIGNMENT ******************)
  18
  19 (* Main properties **********************************************************)
  20
  21 theorem lsubss_trans: ∀h,g,L1,L. h ⊢ L1 •⊑[g] L → ∀L2. h ⊢ L •⊑[g] L2 →
  22                       h ⊢ L1 •⊑[g] L2.
  23 #h #g #L1 #L #H elim H -L1 -L
  24 [ #X #H >(lsubss_inv_atom1 … H) -H //
  25 | #I #L1 #L #W #HL1 #IHL1 #X #H
  26   elim (lsubss_inv_pair1 … H) -H * #L2
  27   [ #HL2 #H destruct /3 width=1/
  28   | #V #l #H1WV #H2WV #HL2 #H1 #H2 destruct /3 width=3/
  29   ]
  30 | #L1 #L #V1 #W1 #l #H1VW1 #H2VW1 #HL1 #IHL1 #X #H
  31   elim (lsubss_inv_pair1 … H) -H * #L2
  32   [ #HL2 #H destruct /3 width=5/
  33   | #V #l0 #_ #_ #_ #_ #H destruct
  34   ]
  35 ]
  36 qed.