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; ACL2 String Library
; Copyright (C) 2009-2013 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>
(in-package "STR")
(include-book "std/basic/defs" :dir :system)
;; Primarily proves transitivity of string< and its behavior on str-fix.
(local (defthm lemma
(implies (and (character-listp x)
(character-listp y)
(character-listp z)
(string<-l x y n)
(string<-l y z n))
(string<-l x z n))
:hints(("Goal" :in-theory (enable string<-l)))))
(local (defthm equal-of-char-code
(implies (and (characterp x)
(characterp y))
(equal (equal (char-code x) (char-code y))
(equal x y)))
:hints (("goal" :use ((:instance code-char-char-code-is-identity
(c x))
(:instance code-char-char-code-is-identity
(c y)))
:in-theory (disable code-char-char-code-is-identity)))))
(local (defthm lemma2
(implies (and (character-listp x)
(character-listp y)
(character-listp z)
(integerp n)
(not (string<-l x y n))
(not (string<-l y z n)))
(not (string<-l x z n)))
:hints(("Goal" :in-theory (enable string<-l)))))
(defthm transitivity-of-string<
(implies (and (string< x y)
(string< y z))
(string< x z))
:hints(("Goal" :in-theory (enable string<))))
(defthm transitivity-of-string<-negated
(implies (and (not (string< x y))
(not (string< y z)))
(not (string< x z)))
:hints(("Goal" :in-theory (enable string<))))
(defthm string<-of-str-fix-1
(equal (string< (str-fix x) y)
(string< x y))
:hints(("Goal" :in-theory (enable string< str-fix))))
(defthm string<-of-str-fix-2
(equal (string< x (str-fix y))
(string< x y))
:hints(("Goal" :in-theory (enable string< str-fix))))
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