|
adamc@616
|
1 (* Copyright (c) 2009, Adam Chlipala
|
|
adamc@616
|
2 * All rights reserved.
|
|
adamc@616
|
3 *
|
|
adamc@616
|
4 * Redistribution and use in source and binary forms, with or without
|
|
adamc@616
|
5 * modification, are permitted provided that the following conditions are met:
|
|
adamc@616
|
6 *
|
|
adamc@616
|
7 * - Redistributions of source code must retain the above copyright notice,
|
|
adamc@616
|
8 * this list of conditions and the following disclaimer.
|
|
adamc@616
|
9 * - Redistributions in binary form must reproduce the above copyright notice,
|
|
adamc@616
|
10 * this list of conditions and the following disclaimer in the documentation
|
|
adamc@616
|
11 * and/or other materials provided with the distribution.
|
|
adamc@616
|
12 * - The names of contributors may not be used to endorse or promote products
|
|
adamc@616
|
13 * derived from this software without specific prior written permission.
|
|
adamc@616
|
14 *
|
|
adamc@616
|
15 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
|
|
adamc@616
|
16 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
|
adamc@616
|
17 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
|
adamc@616
|
18 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
|
|
adamc@616
|
19 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
|
|
adamc@616
|
20 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
|
|
adamc@616
|
21 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
|
|
adamc@616
|
22 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
|
|
adamc@616
|
23 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
|
|
adamc@616
|
24 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
|
adamc@616
|
25 * POSSIBILITY OF SUCH DAMAGE.
|
|
adamc@616
|
26 *)
|
|
adamc@616
|
27
|
|
adamc@616
|
28 Set Implicit Arguments.
|
|
adamc@616
|
29
|
|
adamc@616
|
30
|
|
adamc@616
|
31 Axiom ext_eq : forall dom ran (f g : forall x : dom, ran x),
|
|
adamc@616
|
32 (forall x, f x = g x)
|
|
adamc@616
|
33 -> f = g.
|
|
adamc@616
|
34
|
|
adamc@616
|
35 Theorem ext_eq_forall : forall dom (f g : forall x : dom, Type),
|
|
adamc@616
|
36 (forall x, f x = g x)
|
|
adamc@616
|
37 -> (forall x, f x) = (forall x, g x).
|
|
adamc@616
|
38 intros.
|
|
adamc@616
|
39 rewrite (ext_eq _ f g H); reflexivity.
|
|
adamc@616
|
40 Qed.
|
|
adamc@616
|
41
|
|
adamc@616
|
42 Theorem ext_eq_forallS : forall dom (f g : forall x : dom, Set),
|
|
adamc@616
|
43 (forall x, f x = g x)
|
|
adamc@616
|
44 -> (forall x, f x) = (forall x, g x).
|
|
adamc@616
|
45 intros.
|
|
adamc@616
|
46 rewrite (ext_eq _ f g H); reflexivity.
|
|
adamc@616
|
47 Qed.
|
