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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-4")
(%interactive)
(%autoadmit prefixp)
(%autoprove prefixp-when-not-consp-one
(%restrict default prefixp (equal x 'x)))
(%autoprove prefixp-when-not-consp-two
(%restrict default prefixp (equal x 'x)))
(%autoprove prefixp-of-cons-and-cons
(%restrict default prefixp (equal x '(cons a x)))
(%auto :strategy (cleanup split crewrite)))
(%autoprove booleanp-of-prefixp
(%cdr-cdr-induction x y))
(%autoprove prefixp-of-list-fix-one
(%cdr-cdr-induction x y))
(%autoprove prefixp-of-list-fix-two
(%cdr-cdr-induction x y))
(%autoprove same-length-prefixes-equal-cheap
(%cdr-cdr-induction x y))
(%autoprove prefixp-when-lengths-wrong
(%cdr-cdr-induction x y))
(defsection prefixp-when-lengths-wrong-replacement
;; BOZO see if we still need this? If so, change the ACL2 rule to
;; add a backchain limit. Else, just use the above autoprove.
(%prove (%rule prefixp-when-lengths-wrong-replacement
:hyps (list (%hyp (< (len y) (len x)) :limit 1))
:lhs (prefixp x y)
:rhs nil))
(%auto)
(%qed)
(%disable default prefixp-when-lengths-wrong)
(%enable default prefixp-when-lengths-wrong-replacement))
(%autoadmit prefixp-badguy)
(%autoprove prefixp-badguy-when-not-consp
(%restrict default prefixp-badguy (equal x 'x)))
(%autoprove prefixp-badguy-of-cons
(%restrict default prefixp-badguy (equal x '(cons a x)))
(%auto :strategy (cleanup split crewrite)))
(local (%enable default prefixp-badguy-when-not-consp prefixp-badguy-of-cons))
(%autoprove natp-of-prefixp-badguy
(%cdr-induction x))
(%autoprove lemma-for-prefixp-badguy-index-property
(%induct (rank x)
((not (consp x))
nil)
((consp x)
(((x (cdr x))
(y (cdr y)))))))
(%autoprove lemma-2-for-prefixp-badguy-index-property
(%induct (rank x)
((not (consp x))
nil)
((consp x)
(((x (cdr x))
(y (cdr y)))))))
(%autoprove prefixp-badguy-index-property
(%enable default
lemma-for-prefixp-badguy-index-property
lemma-2-for-prefixp-badguy-index-property))
(%autoprove forcing-prefixp-when-not-prefixp-badguy
(%cdr-cdr-induction x y))
(local (%disable default prefixp-badguy-when-not-consp prefixp-badguy-of-cons))
(%autoprove subsetp-when-prefixp-cheap
(%cdr-cdr-induction x y))
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