matita/matita/contribs/lambdadelta/static_2/syntax/teq_ext_teq_ext.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 "static_2/syntax/teq_teq.ma".
  16 include "static_2/syntax/teq_ext.ma".
  17
  18 (* SYNTACTIC EQUIVALENCE ****************************************************)
  19
  20 (* Main properties **********************************************************)
  21
  22 theorem ceq_ext_trans (I):
  23         ∀L1,I1. L1 ⊢ I1 ≡ I → ∀L2,I2. L2 ⊢ I ≡ I2 → ∀L3. L3 ⊢ I1 ≡ I2.
  24 #I #L1 #I1 * -I1 -I //
  25 #I1 #V1 #V #HV1 #L2 #Z #H
  26 elim (ext2_inv_pair_sn … H) -H #V2 #HV2 #H #L3 destruct
  27 /3 width=3 by ext2_pair, teq_trans/
  28 qed-.