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; Milawa - A Reflective Theorem Prover
; Copyright (C) 2005-2009 Kookamara LLC
;
; Contact:
;
; Kookamara LLC
; 11410 Windermere Meadows
; Austin, TX 78759, USA
; http://www.kookamara.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@kookamara.com>
(in-package "MILAWA")
(include-book "utilities-3")
(%interactive)
(%autoadmit tuplep)
(defmacro %tuplep-induct (n x)
`(%induct (nfix ,n)
((zp ,n)
nil)
((not (zp ,n))
(((,n (- ,n 1))
(,x (cdr ,x)))))))
(%autoprove tuplep-when-not-consp
(%restrict default tuplep (equal n 'n)))
(%autoprove tuplep-when-zp
(%restrict default tuplep (equal n 'n)))
(%autoprove tuplep-of-cons
(%restrict default tuplep (equal n 'n)))
(%autoprove booleanp-of-tuplep
(%tuplep-induct n x))
(%autoprove true-listp-when-tuplep
(%tuplep-induct n x))
(%autoprove len-when-tuplep
(%tuplep-induct n x))
(defthm tuplep-of-len
;; BOZO move to utilities
(equal (tuplep (len x) x)
(true-listp x))
:hints(("Goal" :induct (cdr-induction x))))
(%autoprove tuplep-of-len
(%cdr-induction x)
(%restrict default tuplep (equal x 'x)))
(%autoprove tuplep-when-true-listp
(%tuplep-induct n x))
(%autoprove consp-of-cdr-when-tuplep-2-cheap)
(%autoprove consp-of-cdr-when-tuplep-3-cheap)
(%autoprove consp-of-cdr-of-cdr-when-tuplep-3-cheap)
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