helm/software/matita/tests/overred.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 set "baseuri" "cic:/matita/test/overred/".
  16
  17 include "logic/equality.ma".
  18
  19 axiom T1 : Type.
  20 axiom X : Type.
  21 axiom x : X.
  22 definition T2 : Type := T1.
  23 definition T3 : Type := T2.
  24 axiom t3 : T3.
  25 axiom c : T2 -> X -> X.
  26
  27 coercion cic:/matita/test/overred/c.con 1.
  28
  29 axiom daemon : c t3 x = x.
  30
  31 theorem find_a_coercion_from_T2_for_a_term_in_T3 : (* c *) t3 x = x.
  32 apply daemon.
  33 qed.