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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 nth)
(%autoprove nth-when-zp
(%restrict default nth (equal n 'n)))
(%autoprove nth-of-nfix
(%restrict default nfix (memberp n '(n (nfix n)))))
(%autoprove nth-of-list-fix
(%autoinduct nth)
(%restrict default nth (equal n 'n)))
(%autoprove nth-when-index-too-large
(%autoinduct nth)
(%restrict default nth (equal n 'n)))
(%autoprove nth-of-increment
(%restrict default nth (equal n '(+ '1 n))))
(%autoprove nth-of-app
(%autoinduct nth)
(%restrict default nth (equal n 'n)))
(%autoprove nth-of-rev
(%cdr-induction x)
(%restrict default nth (memberp n '((- n (len x2)) (- (len x2) n)))))
(%autoprove memberp-of-nth
(%autoinduct nth)
(%restrict default nth (equal n 'n)))
;; see also utilities-4.lisp for more theorems about nth
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