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; Lemmas about explode-atom
; Copyright (C) 2005-2006 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>
;
; explode-atom.lisp
; This file was originally part of the Unicode library.
(in-package "ACL2")
(include-book "decimal")
(local (include-book "std/lists/append" :dir :system))
(local (include-book "explode-nonnegative-integer"))
(defthm true-listp-of-explode-atom
(true-listp (explode-atom x base))
:rule-classes :type-prescription)
(defthm consp-of-explode-atom-when-integerp
(implies (integerp n)
(consp (explode-atom n base)))
:rule-classes :type-prescription)
(defthm equal-of-explode-atoms-when-natps
(implies (and (natp n)
(natp m)
(force (print-base-p base)))
(equal (equal (explode-atom n base)
(explode-atom m base))
(equal n m))))
(defthm nonzeroness-of-explode-atom-when-not-zp
(implies (and (not (zp n))
(force (print-base-p base)))
(not (equal (explode-atom n base) '(#\0)))))
(defthm digit-listp-of-explode-atom
(implies (natp n)
(str::digit-listp (explode-atom n 10))))
(defthm character-listp-of-explode-atom
(character-listp (explode-atom x base))
:hints(("Goal" :in-theory (disable explode-nonnegative-integer))))
; Copied from std/io/base.lisp, wherein it was added by Matt K. for princ$
; change 12/7/2012.
(defthm character-listp-explode-atom+
(character-listp (explode-atom+ x base radix)))
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