; 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
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; 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)
