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; ACL2 String Library
; Copyright (C) 2009-2014 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: Jared Davis <jared@centtech.com>
(in-package "STR")
(include-book "std/basic/defs" :dir :system)
(include-book "std/util/define" :dir :system)
(defsection code-char-lemmas
:parents (code-char)
:short "Lemmas about @(see code-char) from the @(see std/strings) library."
(defthm default-code-char
(implies (or (zp x)
(not (< x 256)))
(equal (code-char x)
(code-char 0)))
:hints(("Goal" :use ((:instance completion-of-code-char)))))
(local (defthm l0
(implies (not (or (zp x)
(not (< x 256))))
(not (equal (code-char x)
(code-char 0))))
:hints(("Goal" :use ((:instance char-code-code-char-is-identity (n x)))))))
(local (defthm l1
(equal (equal (code-char x)
(code-char 0))
(or (zp x)
(not (< x 256))))))
(local (defthm l2
(implies (and (natp n)
(natp m)
(< n 256)
(< m 256))
(equal (equal (code-char n) (code-char m))
(equal n m)))
:hints(("Goal"
:in-theory (disable char-code-code-char-is-identity)
:use ((:instance char-code-code-char-is-identity (n n))
(:instance char-code-code-char-is-identity (n m)))))))
(defthm equal-of-code-char-and-code-char
(equal (equal (code-char x) (code-char y))
(let ((zero-x (or (zp x) (>= x 256)))
(zero-y (or (zp y) (>= y 256))))
(if zero-x
zero-y
(equal x y))))
:hints(("Goal"
:in-theory (disable l2)
:use ((:instance l2 (n x) (m y))))))
(defthm equal-of-code-code-and-constant
(implies (syntaxp (quotep c))
(equal (equal (code-char x) c)
(and (characterp c)
(if (equal c (code-char 0))
(or (zp x)
(not (< x 256)))
(equal x (char-code c))))))
:hints(("goal" :use ((:instance completion-of-code-char))))))
(defsection char-code-lemmas
:parents (char-code)
:short "Lemmas about @(see char-code) from the @(see std/strings) library."
(defthm equal-of-char-code-and-constant
(implies (syntaxp (quotep c))
(equal (equal (char-code x) c)
(if (characterp x)
(and (natp c)
(<= c 255)
(equal x (code-char c)))
(equal c 0)))))
(local (defthm l0
(implies (and (characterp x)
(characterp y))
(equal (equal (char-code x) (char-code y))
(equal x y)))
:hints(("Goal" :use acl2::equal-char-code))))
(defthm equal-of-char-codes
(equal (equal (char-code x) (char-code y))
(equal (char-fix x)
(char-fix y)))
:hints(("Goal" :in-theory (enable char-fix)))))
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