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; Std/basic - Basic definitions
;
; Copyright (C) 2014 Centaur Technology
;
; Contact:
; Centaur Technology Formal Verification Group
; 7600-C N. Capital of Texas Highway, Suite 300, Austin, TX 78731, USA.
; http://www.centtech.com/
;
; License: (An MIT/X11-style license)
;
; Permission is hereby granted, free of charge, to any person obtaining a
; copy of this software and associated documentation files (the "Software"),
; to deal in the Software without restriction, including without limitation
; the rights to use, copy, modify, merge, publish, distribute, sublicense,
; and/or sell copies of the Software, and to permit persons to whom the
; Software is furnished to do so, subject to the following conditions:
;
; The above copyright notice and this permission notice shall be included in
; all copies or substantial portions of the Software.
;
; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
; IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
; AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
; FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
; DEALINGS IN THE SOFTWARE.
;
; Original author: Sol Swords <sswords@centtech.com>
; Contributing author: Alessandro Coglio <coglio@kestrel.edu>
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(in-package "ACL2")
(include-book "xdoc/top" :dir :system)
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(defsection pos-fix
:parents (posp)
:short "@(call pos-fix) is a fixing function for @(see posp): it is the
identity for positive integers, or returns 1 for any other object."
:long "<p>This has guard @('t'). For better efficiency, see @(see lposfix).</p>"
(defund pos-fix (x)
(declare (xargs :guard t))
(if (posp x) x 1))
(local (in-theory (enable pos-fix)))
(defthm posp-of-pos-fix
(posp (pos-fix x))
:rule-classes :type-prescription)
(defthm pos-fix-when-posp
(implies (posp x)
(equal (pos-fix x) x))))
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