matita/matita/contribs/lambdadelta/basic_2/static/lsuba_lsuba.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/lsuba_aaa.ma".
  16
  17 (* LOCAL ENVIRONMENT REFINEMENT FOR ATOMIC ARITY ASSIGNMENT *****************)
  18
  19 (* Main properties **********************************************************)
  20
  21 theorem lsuba_trans: ∀L1,L. L1 ⁝⊑ L → ∀L2. L ⁝⊑ L2 → L1 ⁝⊑ L2.
  22 #L1 #L #H elim H -L1 -L
  23 [ #X #H >(lsuba_inv_atom1 … H) -H //
  24 | #I #L1 #L #V #HL1 #IHL1 #X #H
  25   elim (lsuba_inv_pair1 … H) -H * #L2
  26   [ #HL2 #H destruct /3 width=1/
  27   | #V #A #HLV #HL2V #HL2 #H1 #H2 destruct /3 width=3/
  28   ]
  29 | #L1 #L #V1 #W #A1 #HV1 #HW #HL1 #IHL1 #X #H
  30   elim (lsuba_inv_pair1 … H) -H * #L2
  31   [ #HL2 #H destruct /3 width=5/
  32   | #V #A2 #_ #_ #_ #_ #H destruct
  33   ]
  34 ]
  35 qed.