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; Centaur Lexer Library
; Copyright (C) 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: Jared Davis <jared@centtech.com>
(in-package "ACL2")
(include-book "std/util/defrule" :dir :system)
(include-book "std/lists/top" :dir :system)
(include-book "std/strings/arithmetic" :dir :system)
(include-book "std/basic/arith-equivs" :dir :system)
(local (include-book "arithmetic/top-with-meta" :dir :system))
(in-theory (disable nth
update-nth
;; These can interfere with stobj stuff
nth-0-cons
nth-when-zp
nth-add1))
(local (in-theory (enable nthcdr len nth)))
(defrule nthcdr-of-len
(implies (true-listp x)
(equal (nthcdr (len x) x)
nil)))
(defrule nthcdr-of-len-free
(implies (and (equal n (len x))
(true-listp x))
(equal (nthcdr n x)
nil)))
(defrule cdr-of-nthcdr
(equal (cdr (nthcdr n x))
(nthcdr (+ 1 (nfix n)) x)))
(defrule nth-when-index-too-big
(implies (<= (len x) (nfix n))
(equal (nth n x)
nil)))
;; now part of std/lists
;; (defrule nth-of-nthcdr
;; (equal (nth a (nthcdr b x))
;; (nth (+ (nfix a) (nfix b)) x))
;; :disable (acl2::nthcdr-of-cdr))
(defrule nthcdr-under-iff-when-true-listp
(implies (true-listp x)
(iff (nthcdr n x)
(< (nfix n) (len x)))))
(defthm true-listp-when-character-listp
(implies (character-listp x)
(true-listp x)))
(defthm character-listp-of-nthcdr
(implies (character-listp x)
(character-listp (nthcdr n x)))
:hints(("Goal" :in-theory (disable acl2::cdr-of-nthcdr))))
(defthm character-listp-of-take
(implies (character-listp x)
(equal (character-listp (take n x))
(<= (nfix n) (len x)))))
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