/usr/share/acl2-6.3/books/str/iprefixp.lisp is in acl2-books-source 6.3-5.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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; Copyright (C) 2009-2013 Centaur Technology
;
; Contact:
; Centaur Technology Formal Verification Group
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; http://www.centtech.com/
;
; 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
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; 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., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA.
;
; Original author: Jared Davis <jared@centtech.com>
(in-package "STR")
(include-book "ieqv")
(include-book "std/lists/prefixp" :dir :system)
(local (include-book "arithmetic"))
(defsection iprefixp
:parents (substrings)
:short "Case-insensitive character-list prefix test."
:long "<p>@(call iprefixp) determines whether one character list is a prefix
of another, where each character is tested using @(see ichareqv).</p>"
(defund iprefixp (x y)
(declare (xargs :guard (and (character-listp x)
(character-listp y))))
(if (consp x)
(and (consp y)
(ichareqv (car x) (car y))
(iprefixp (cdr x) (cdr y)))
t))
(local (in-theory (enable iprefixp)))
(defthm iprefixp-when-not-consp-left
(implies (not (consp x))
(iprefixp x y)))
(defthm iprefixp-of-cons-left
(equal (iprefixp (cons a x) y)
(and (consp y)
(ichareqv a (car y))
(iprefixp x (cdr y)))))
(defthm iprefixp-when-not-consp-right
(implies (not (consp y))
(equal (iprefixp x y)
(not (consp x))))
:hints(("Goal" :induct (len x))))
(defthm iprefixp-of-cons-right
(equal (iprefixp x (cons a y))
(if (consp x)
(and (ichareqv (car x) a)
(iprefixp (cdr x) y))
t)))
(defthm iprefixp-of-list-fix-left
(equal (iprefixp (list-fix x) y)
(iprefixp x y)))
(defthm iprefixp-of-list-fix-right
(equal (iprefixp x (list-fix y))
(iprefixp x y)))
(defcong icharlisteqv equal (iprefixp x y) 1)
(defcong icharlisteqv equal (iprefixp x y) 2)
(defthm iprefixp-when-prefixp
(implies (prefixp x y) (iprefixp x y))))
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