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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")
(encapsulate
()
(local (include-book "arithmetic-3/bind-free/top" :dir :system))
(defthm nthcdr-of-non-consp
(implies (not (consp x))
(equal (nthcdr n x)
(if (zp n)
x
nil)))
:hints (("Goal" :in-theory (enable nthcdr))))
(defthm consp-of-nthcdr
(equal (consp (nthcdr n l))
(< (nfix n) (len l)))
:hints (("Goal" :in-theory (enable nthcdr)))))
;; arithmetic-3 loops??
(defthm len-of-nthcdr
(equal (len (nthcdr n l))
(if (natp n)
(max 0 (- (len l) n))
(len l)))
:hints (("Goal" :in-theory (enable nthcdr))))
(defthm nthcdr-of-1
(equal (nthcdr 1 x)
(cdr x)))
(defthm nthcdr-of-2
(equal (nthcdr 2 x)
(cddr x)))
(defthm nthcdr-of-3
(equal (nthcdr 3 x)
(cdddr x)))
(defthm nthcdr-of-4
(equal (nthcdr 4 x)
(cddddr x)))
(local (defthm acl2-count-of-cdr
(implies (consp x)
(< (acl2-count (cdr x))
(acl2-count x)))
:rule-classes :linear))
(local (defthm acl2-count-of-cdr-weak
(<= (acl2-count (cdr x))
(acl2-count x))
:rule-classes :linear))
(local (defthm acl2-count-of-consp-positive
(implies (consp x)
(< 0 (acl2-count x)))
:rule-classes :linear))
(defthm acl2-count-of-nthcdr-rewrite
(equal (< (acl2-count (nthcdr n x))
(acl2-count x))
(if (zp n)
nil
(or (consp x)
(< 0 (acl2-count x))))))
(defthm acl2-count-of-nthcdr-linear
(implies (and (not (zp n))
(consp x))
(< (acl2-count (nthcdr n x))
(acl2-count x)))
:rule-classes :linear)
(defthm acl2-count-of-nthcdr-linear-weak
(<= (acl2-count (nthcdr n x))
(acl2-count x))
:rule-classes :linear)
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