matita/matita/contribs/lambdadelta/basic_2A/grammar/tsts_tsts.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   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       *)
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  14
  15 include "basic_2A/grammar/tsts.ma".
  16
  17 (* SAME TOP TERM STRUCTURE **************************************************)
  18
  19 (* Main properties **********************************************************)
  20
  21 (* Basic_1: was: iso_trans *)
  22 theorem tsts_trans: Transitive … tsts.
  23 #T1 #T * -T1 -T //
  24 #I #V1 #V #T1 #T #X #H
  25 elim (tsts_inv_pair1 … H) -H #V2 #T2 #H destruct //
  26 qed-.
  27
  28 theorem tsts_canc_sn: ∀T,T1. T ≂ T1 → ∀T2. T ≂ T2 → T1 ≂ T2.
  29 /3 width=3 by tsts_trans, tsts_sym/ qed-.
  30
  31 theorem tsts_canc_dx: ∀T1,T. T1 ≂ T → ∀T2. T2 ≂ T → T1 ≂ T2.
  32 /3 width=3 by tsts_trans, tsts_sym/ qed-.