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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 "deflist")
(include-book "strip-firsts")
(include-book "strip-seconds")
(include-book "strip-lens")
(%interactive)
(%deflist true-list-listp (x)
(true-listp x))
(%deflist tuple-listp (n x)
(tuplep n x))
(%autoprove rank-of-strip-firsts-when-tuple-listp-2
(%cdr-induction x))
(%autoprove rank-of-strip-seconds-when-tuple-listp-2
(%cdr-induction x))
(%autoprove strip-lens-when-tuple-listp
(%cdr-induction x)
(%auto)
(%fertilize (strip-lens x2) (repeat (nfix n) (len x2))))
(%autoadmit list2-list)
(%autoprove list2-list-when-not-consp-one
(%restrict default list2-list (equal x 'x)))
(%autoprove list2-list-when-not-consp-two
(%restrict default list2-list (equal x 'x)))
(%autoprove list2-list-of-cons-and-cons
(%restrict default list2-list (equal x '(cons a x))))
(%autoprove true-listp-of-list2-list
(%cdr-cdr-induction x y))
(%autoprove true-listp-list-of-list2-list
(%cdr-cdr-induction x y))
(%autoprove list2-list-of-list-fix-one
(%cdr-cdr-induction x y))
(%autoprove list2-list-of-list-fix-two
(%cdr-cdr-induction x y))
(%autoprove len-of-list2-list
(%cdr-cdr-induction x y))
(%autoprove strip-lens-of-list2-list
(%cdr-cdr-induction x y))
(defsection more-than-two-when-not-zero-one-or-two
;; This isn't needed in ACL2. not sure why we need it.
;; BOZO might this have to do with our missing rule?
(%prove (%rule more-than-two-when-not-zero-one-or-two
:hyps (list (%hyp (not (zp n)))
(%hyp (not (equal 1 n)))
(%hyp (not (equal 2 n))))
:lhs (< 2 n)
:rhs t))
(%use (%instance (%thm squeeze-law-one) (b 2) (a n)))
(%auto)
(%qed))
(%autoprove tuple-listp-of-list2-list
(%cdr-cdr-induction x y)
(%enable default more-than-two-when-not-zero-one-or-two))
(%autoprove forcing-strip-firsts-of-list2-list
(%cdr-cdr-induction x y))
(%autoprove forcing-strip-seconds-of-list2-list
(%cdr-cdr-induction x y))
(%ensure-exactly-these-rules-are-missing "../../utilities/tuple-listp")
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