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;; 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")
(local (include-book "arithmetic-3/bind-free/top" :dir :system))
(local (defthm len-when-consp
(implies (consp x)
(< 0 (len x)))
:rule-classes ((:linear) (:rewrite))))
(defthm true-listp-of-append
(equal (true-listp (append x y))
(true-listp y)))
(defthm consp-of-append
(equal (consp (append x y))
(or (consp x)
(consp y))))
(defthm len-of-append
(equal (len (append x y))
(+ (len x) (len y))))
(defthm nth-of-append
(equal (nth n (append x y))
(if (< (nfix n) (len x))
(nth n x)
(nth (- n (len x)) y))))
(defthm equal-when-append-same
(equal (equal (append x y1)
(append x y2))
(equal y1 y2)))
(local (defthm append-nonempty-list
(implies (consp x)
(not (equal (append x y) y)))
:hints(("Goal" :use ((:instance len (x (append x y)))
(:instance len (x y)))))))
(local (defun cdr-cdr-induction (a b)
(declare (xargs :guard t))
(if (and (consp a)
(consp b))
(cdr-cdr-induction (cdr a) (cdr b))
nil)))
(defthm equal-of-appends-when-true-listps
(implies (and (true-listp x1)
(true-listp x2))
(equal (equal (append x1 y)
(append x2 y))
(equal x1 x2)))
:hints(("Goal" :induct (cdr-cdr-induction x1 x2))))
(defthm character-listp-of-append
(implies (and (character-listp x)
(character-listp y))
(character-listp (append x y))))
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