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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 remove-all)
(%autoprove remove-all-when-not-consp
(%restrict default remove-all (equal x 'x)))
(%autoprove remove-all-of-cons
(%restrict default remove-all (equal x '(cons b x))))
(%autoprove remove-all-of-list-fix
(%cdr-induction x))
(%autoprove true-listp-of-remove-all
(%cdr-induction x))
(%autoprove memberp-of-remove-all
(%cdr-induction x))
(%autoprove remove-all-of-app
(%cdr-induction x))
(%autoprove rev-of-remove-all
(%cdr-induction x))
(%autoprove subsetp-of-remove-all-with-x
(%cdr-induction x))
(%autoprove subsetp-of-remove-all-with-remove-all
(%use (%instance (%thm subsetp-badguy-membership-property)
(x (remove-all a x))
(y (remove-all a y)))))
(%autoprove subsetp-of-remove-all-when-subsetp)
(%autoprove remove-all-of-non-memberp
(%cdr-induction x))
(%autoprove remove-all-of-remove-all
(%cdr-induction x))
(%autoprove subsetp-of-cons-and-remove-all-two
(%use (%instance (%thm subsetp-badguy-membership-property)
(x (cons a y))
(y (cons a (remove-all a y))))))
(%autoprove lemma-for-equal-of-len-of-remove-all-and-len
(%cdr-induction x))
(%autoprove equal-of-len-of-remove-all-and-len
(%enable default lemma-for-equal-of-len-of-remove-all-and-len))
(%autoadmit fast-remove-all$)
(%autoprove fast-remove-all$-when-not-consp
(%restrict default fast-remove-all$ (equal x 'x)))
(%autoprove fast-remove-all$-of-cons
(%restrict default fast-remove-all$ (equal x '(cons b x))))
(%autoprove forcing-fast-remove-all$-removal
(%autoinduct fast-remove-all$)
(%enable default fast-remove-all$-when-not-consp fast-remove-all$-of-cons))
|
