/usr/share/acl2-4.3/books/unicode/prefixp.lisp is in acl2-books-source 4.3-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 | ;; Processing Unicode Files with ACL2
;; Copyright (C) 2005-2006 by Jared Davis <jared@cs.utexas.edu>
;;
;; This program is free software; you can redistribute it and/or modify it
;; under the terms of the GNU General Public License as published by the Free
;; Software Foundation; either version 2 of the License, or (at your option)
;; any later version.
;;
;; This program is distributed in the hope that it will be useful but WITHOUT
;; ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
;; FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
;; more details.
;;
;; You should have received a copy of the GNU General Public License along with
;; this program; if not, write to the Free Software Foundation, Inc., 59 Temple
;; Place - Suite 330, Boston, MA 02111-1307, USA.
(in-package "ACL2")
(include-book "list-fix")
(local (include-book "take"))
(local (include-book "arithmetic/top" :dir :system))
(defund prefixp (x y)
(declare (xargs :guard t))
(if (consp x)
(and (consp y)
(equal (car x) (car y))
(prefixp (cdr x) (cdr y)))
t))
(defthm prefixp-when-not-consp-left
(implies (not (consp x))
(prefixp x y))
:hints(("Goal" :in-theory (enable prefixp))))
(defthm prefixp-of-cons-left
(equal (prefixp (cons a x) y)
(and (consp y)
(equal a (car y))
(prefixp x (cdr y))))
:hints(("Goal" :in-theory (enable prefixp))))
(defthm prefixp-when-not-consp-right
(implies (not (consp y))
(equal (prefixp x y)
(not (consp x))))
:hints(("Goal" :induct (len x))))
(defthm prefixp-of-cons-right
(equal (prefixp x (cons a y))
(if (consp x)
(and (equal (car x) a)
(prefixp (cdr x) y))
t)))
(defthm prefixp-of-list-fix-left
(equal (prefixp (list-fix x) y)
(prefixp x y))
:hints(("Goal" :in-theory (enable prefixp))))
(defthm prefixp-of-list-fix-right
(equal (prefixp x (list-fix y))
(prefixp x y))
:hints(("Goal" :in-theory (enable prefixp))))
(defthm len-when-prefixp
(implies (prefixp x y)
(equal (< (len y) (len x))
nil))
:rule-classes ((:rewrite)
(:linear :corollary (implies (prefixp x y)
(<= (len x) (len y)))))
:hints(("Goal" :in-theory (enable (:induction prefixp)))))
(defthm simpler-take-when-prefixp
(implies (prefixp x y)
(equal (simpler-take (len x) y)
(list-fix x)))
:hints(("Goal"
:in-theory (enable (:induction prefixp)
simpler-take))))
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