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author | Ziv Scully <ziv@mit.edu> |
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date | Mon, 21 Sep 2015 10:16:55 -0400 |

parents | be88d2d169f6 |

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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. *) 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.