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+(* Copyright (c) 2009, Adam Chlipala
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *
+ * - Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * - Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * - The names of contributors may not be used to endorse or promote products
+ *   derived from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+ * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+ * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 
+ * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+ * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+ * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+ * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+ * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *)
+
+Require Import Syntax.
+
+Set Implicit Arguments.
+
+
+Axiom ext_eq : forall dom ran (f g : forall x : dom, ran x),
+  (forall x, f x = g x)
+  -> f = g.
+
+Theorem ext_eq_forall : forall dom (f g : forall x : dom, Type),
+  (forall x, f x = g x)
+  -> (forall x, f x) = (forall x, g x).
+  intros.
+  rewrite (ext_eq _ f g H); reflexivity.
+Qed.
+
+Theorem ext_eq_forallS : forall dom (f g : forall x : dom, Set),
+  (forall x, f x = g x)
+  -> (forall x, f x) = (forall x, g x).
+  intros.
+  rewrite (ext_eq _ f g H); reflexivity.
+Qed.