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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-1")
(%interactive)
(defsection equal-of-cdr-and-self
;; BOZO I don't have this rule in ACL2. Maybe I should add it?
;; BOZO Move this to primitives somewhere
(%prove (%rule equal-of-cdr-and-self
:lhs (equal x (cdr x))
:rhs (not x)))
(local (%disable default rank-of-cdr [outside]rank-of-cdr))
(%use (%instance (%thm rank-of-cdr)))
(%auto)
(%qed)
(%enable default equal-of-cdr-and-self))
(%autoadmit app)
(%autoprove app-when-not-consp
(%restrict default app (equal x 'x)))
(%autoprove app-of-cons
(%restrict default app (equal x '(cons a x))))
(%autoprove app-of-list-fix-one
(%cdr-induction x))
(%autoprove app-of-list-fix-two
(%cdr-induction x))
(%autoprove app-when-not-consp-two
(%cdr-induction x))
(%autoprove app-of-singleton-list-cheap)
(%autoprove true-listp-of-app
(%cdr-induction x))
(%autoprove app-of-app
(%cdr-induction x))
(%autoprove memberp-of-app
(%cdr-induction x))
(%autoprove consp-of-app)
(%autoprove app-under-iff)
(%autoprove len-of-app
(%cdr-induction x))
(%autoprove subsetp-of-app-one
(%cdr-induction x))
(%autoprove subsetp-of-app-two
(%use (%instance (%thm subsetp-badguy-membership-property) (x x) (y (app x y)))))
(%autoprove subsetp-of-app-three
(%use (%instance (%thm subsetp-badguy-membership-property) (x y) (y (app x y)))))
(%autoprove subsetp-of-app-when-subsets
(%use (%instance (%thm subsetp-badguy-membership-property) (x (app x w)) (y (app y z)))))
(%autoprove subsetp-of-symmetric-apps
(%use (%instance (%thm subsetp-badguy-membership-property) (x (app x y)) (y (app y x)))))
(%autoprove weirdo-rule-for-subsetp-of-app-one)
(%autoprove weirdo-rule-for-subsetp-of-app-two)
(%autoprove cdr-of-app-when-x-is-consp)
(%autoprove car-of-app-when-x-is-consp)
(%autoprove memberp-of-app-onto-singleton)
(%autoprove subsetp-of-app-onto-singleton-with-cons
(%use (%instance (%thm subsetp-badguy-membership-property) (x (app x (list a))) (y (cons a x)))))
(%autoprove subsetp-of-cons-with-app-onto-singleton
(%use (%instance (%thm subsetp-badguy-membership-property) (x (cons a x)) (y (app x (list a))))))
(%autoprove subsetp-of-cons-of-app-of-app-one
(%use (%instance (%thm subsetp-badguy-membership-property) (x x) (y (cons b (app y (app x z)))))))
(%autoprove subsetp-of-cons-of-app-of-app-two
(%use (%instance (%thm subsetp-badguy-membership-property) (x x) (y (cons a (app y (app z x)))))))
(%autoprove subsetp-of-app-of-app-when-subsetp-one
(%use (%instance (%thm subsetp-badguy-membership-property) (x x) (y (app a (app y b))))))
(%autoprove subsetp-of-app-of-app-when-subsetp-two
(%use (%instance (%thm subsetp-badguy-membership-property) (x x) (y (app a (app b y))))))
(%autoprove app-of-cons-of-list-fix-right
(%cdr-induction x))
(%autoprove app-of-cons-when-not-consp-right
(%cdr-induction x))
(%autoprove equal-of-app-and-app-when-equal-lens
(%cdr-cdr-induction a c))
(%autoprove lemma-for-equal-of-app-and-self
(%cdr-induction x))
(%autoprove equal-of-app-and-self
(%cdr-induction x)
(%enable default lemma-for-equal-of-app-and-self)
(%auto :strategy (cleanup urewrite split crewrite)) ;; elim uglies it up
(%use (%instance (%thm len-of-app)))
(%use (%instance (%thm len-of-app) (x (cdr x))))
(%disable default len-of-app [outside]len-of-app))
|
