branch for universe

[helm.git] / matita / tests / overred.ma

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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+
+
+include "logic/equality.ma".
+
+axiom T1 : Type.
+axiom X : Type.
+axiom x : X.
+definition T2 : Type := T1.
+definition T3 : Type := T2.
+axiom t3 : T3.
+axiom c : T2 -> X -> X.
+
+coercion cic:/matita/tests/overred/c.con 1.
+
+axiom daemon : c t3 x = x. 
+
+theorem find_a_coercion_from_T2_for_a_term_in_T3 : (* c *) t3 x = x.
+apply daemon.
+qed.