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; True-Listp Lemmas
; Copyright (C) 2008-2013 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 "xdoc/top" :dir :system)
(include-book "std/lists/list-defuns" :dir :system)
(in-theory (disable true-listp))
(defsection std/lists/true-listp
:parents (std/lists true-listp)
:short "Lemmas about @(see true-listp) available in the @(see std/lists)
library."
:long "<p>Note: the list of lemmas below is quite incomplete. For instance,
the @(see true-listp) rule about @(see append) will be found in the
documentation for @(see std/lists/append), instead of here.</p>"
(local (in-theory (enable true-listp)))
(defthm true-listp-when-atom
(implies (atom x)
(equal (true-listp x)
(not x))))
(defthm true-listp-of-cons
(equal (true-listp (cons a x))
(true-listp x)))
(defthm consp-under-iff-when-true-listp
;; BOZO even with the backchain limit, this rule can get too expensive.
(implies (true-listp x)
(iff (consp x)
x))
:rule-classes ((:rewrite :backchain-limit-lst 0))))
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