matita/matita/contribs/lambdadelta/basic_2A/etc/fpn/bteq_bteq.etc

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
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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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  13 (**************************************************************************)
  14
  15 include "basic_2/grammar/bteq.ma".
  16
  17 (* EQUIVALENT "BIG TREE" NORMAL FORMS ***************************************)
  18
  19 (* Main properties **********************************************************)
  20
  21 theorem bteq_trans: tri_transitive … bteq.
  22 #G1 #G #L1 #L #T1 #T * //
  23 qed-.
  24
  25 theorem bteq_canc_sn: ∀G,G1,G2,L,L1,L2,T,T1,T2. ⦃G, L, T⦄ ⋕ ⦃G1, L1, T1⦄ →
  26                       ⦃G, L, T⦄ ⋕ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⋕ ⦃G2, L2, T2⦄.
  27 /3 width=5 by bteq_trans, bteq_sym/ qed-.
  28
  29 theorem bteq_canc_dx: ∀G1,G2,G,L1,L2,L,T1,T2,T. ⦃G1, L1, T1⦄ ⋕ ⦃G, L, T⦄ →
  30                       ⦃G2, L2, T2⦄ ⋕ ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ ⋕ ⦃G2, L2, T2⦄.
  31 /3 width=5 by bteq_trans, bteq_sym/ qed-.