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; Milawa - A Reflective Theorem Prover
; Copyright (C) 2005-2009 Kookamara LLC
;
; Contact:
;
; Kookamara LLC
; 11410 Windermere Meadows
; Austin, TX 78759, USA
; http://www.kookamara.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: Jared Davis <jared@kookamara.com>
(in-package "MILAWA")
(include-book "expt")
(include-book "dividesp")
(set-verify-guards-eagerness 2)
(set-case-split-limitations nil)
(set-well-founded-relation ord<)
(set-measure-function rank)
(local (in-theory (enable definition-of-bitwise-and)))
(defthm natp-of-bitwise-and
(equal (natp (bitwise-and a b))
t))
(defthm bitwise-and-when-not-natp-left-cheap
(implies (not (natp a))
(equal (bitwise-and a b)
0))
:rule-classes ((:rewrite :backchain-limit-lst 0)))
(defthm bitwise-and-when-not-natp-right-cheap
(implies (not (natp b))
(equal (bitwise-and a b)
0))
:rule-classes ((:rewrite :backchain-limit-lst 0)))
(defthm |(bitwise-and 0 a)|
(equal (bitwise-and 0 a)
0))
(defthm |(bitwise-and a 0)|
(equal (bitwise-and a 0)
0))
;; (defthm |(bitwise-and 1 a)|
;; (equal (bitwise-and 1 a)
;; (not (dividesp 2 a)))
;; :hints(("Goal" :in-theory (enable dividesp))))
(defthm natp-of-bitwise-or
(equal (natp (bitwise-or a b))
t)
:hints(("Goal" :in-theory (enable definition-of-bitwise-or))))
(defthm natp-of-bitwise-xor
(equal (natp (bitwise-xor a b))
t)
:hints(("Goal" :in-theory (enable definition-of-bitwise-xor))))
(defthm booleanp-of-bitwise-nth
(equal (booleanp (bitwise-nth a b))
t)
:hints(("Goal" :in-theory (enable definition-of-bitwise-nth))))
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