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+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+Inductive T : Set := A: T | B :T->T.
+
+Lemma lem1 : (x,y:T){x=y}+{~x=y}.
+Decide Equality.
+Qed.
+
+Lemma lem2 : (x,y:T){x=y}+{~x=y}.
+Intros x y.
+Decide Equality x y.
+Qed.
+
+Lemma lem3 : (x,y:T){x=y}+{~x=y}.
+Intros x y.
+Decide Equality y x.
+Qed.
+
+Lemma lem4 : (x,y:T){x=y}+{~x=y}.
+Intros x y.
+Compare x y; Auto.
+Qed.
+