matita/matita/contribs/lambda_delta/basic_2/grammar/tstc_tstc.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/grammar/tstc.ma".
  16
  17 (* SAME TOP TERM CONSTRUCTOR ************************************************)
  18
  19 (* Main properties **********************************************************)
  20
  21 (* Basic_1: was: iso_trans *)
  22 theorem tstc_trans: ∀T1,T. T1 ≃ T → ∀T2. T ≃ T2 → T1 ≃ T2.
  23 #T1 #T * -T1 -T //
  24 #I #V1 #V #T1 #T #X #H
  25 elim (tstc_inv_pair1 … H) -H #V2 #T2 #H destruct //
  26 qed.
  27
  28 theorem tstc_canc_sn: ∀T,T1. T ≃ T1 → ∀T2. T ≃ T2 → T1 ≃ T2.
  29 /3 width=3/ qed.
  30
  31 theorem tstc_canc_dx: ∀T1,T. T1 ≃ T → ∀T2. T2 ≃ T → T1 ≃ T2.
  32 /3 width=3/ qed.