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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-2")
(%interactive)
(%autoadmit rev)
(%autoprove rev-when-not-consp
(%restrict default rev (equal x 'x)))
(%autoprove rev-of-cons
(%restrict default rev (equal x '(cons a x))))
(%autoprove rev-of-list-fix
(%cdr-induction x))
(%autoprove true-listp-of-rev
(%car-cdr-elim x))
(%autoprove rev-under-iff)
(%autoprove len-of-rev
(%cdr-induction x))
(%autoprove memberp-of-rev
(%cdr-induction x))
(%autoprove memberp-of-first-of-rev
(%cdr-induction x))
(%autoprove subsetp-of-rev-one
(%use (%instance (%thm subsetp-badguy-membership-property) (x (rev x)) (y x)))
(%use (%instance (%thm subsetp-badguy-membership-property) (x x) (y (rev x)))))
(%autoprove subsetp-of-rev-two
(%use (%instance (%thm subsetp-badguy-membership-property) (x y) (y (rev y))))
(%use (%instance (%thm subsetp-badguy-membership-property) (x (rev y)) (y y))))
(%autoprove lemma-for-rev-of-rev
(%cdr-induction x))
(%autoprove rev-of-rev
(%cdr-induction x)
(%enable default lemma-for-rev-of-rev))
(%autoprove rev-of-app
(%cdr-induction x)
(%auto)
(%fertilize (rev (app x2 y)) (app (rev y) (rev x2))))
(%autoprove subsetp-of-app-of-rev-of-self-one
(%cdr-induction x))
(%autoprove subsetp-of-app-of-rev-of-self-two
(%cdr-induction x))
(%autoadmit revappend)
(%autoprove revappend-when-not-consp
(%restrict default revappend (equal x 'x)))
(%autoprove revappend-of-cons
(%restrict default revappend (equal x '(cons a x))))
(%autoprove forcing-revappend-removal
(%autoinduct revappend)
(%enable default revappend-when-not-consp revappend-of-cons))
(%autoadmit fast-rev)
(%autoprove fast-rev-removal
(%enable default fast-rev))
(%autoadmit fast-app)
(%autoprove fast-app-removal
(%enable default fast-app))
|
