matita/matita/contribs/lambdadelta/basic_2/etc/lcoeq/lcoeq_lcoeq.etc

   1 (**************************************************************************)
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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  14
  15 include "basic_2/grammar/lcoeq.ma".
  16
  17 (* COEQUIVALENCE FOR LOCAL ENVIRONMENTS *************************************)
  18
  19 (* Main properties **********************************************************)
  20
  21 theorem lcoeq_trans: ∀d,e. Transitive … (lcoeq d e).
  22 #d #e #L1 #L2 #H elim H -L1 -L2 -d -e //
  23 [ #I #L1 #L #V #HL1 #_ #X #H >(lcoeq_inv_O2 … HL1) -HL1 //
  24 | #I1 #I #L1 #L #V1 #V #e #_ #IHL1 #X #H elim (lcoeq_inv_pair1 … H) -H //
  25   #I2 #L2 #V2 #HL2 #H destruct /3 width=1 by lcoeq_pair/
  26 | #I #L1 #L #V #d #e #_ #IHL1 #X #H elim (lcoeq_inv_succ1 … H) -H //
  27   #L2 #HL2 #H destruct /3 width=1 by lcoeq_succ/
  28 ]
  29 qed-.