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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 "cons-listp")
(%interactive)
(%deflist member-of-nonep (e x)
(memberp e x)
:negatedp t)
(%autoadmit lists-lookup)
(%autoprove lists-lookup-when-not-consp (%restrict default lists-lookup (equal xs 'xs)))
(%autoprove lists-lookup-of-cons (%restrict default lists-lookup (equal xs '(cons x xs))))
(%autoprove lists-lookup-of-list-fix (%cdr-induction xs))
(%autoprove lists-lookup-of-app (%cdr-induction xs))
(%autoprove consp-of-lists-lookup (%cdr-induction xs))
(%autoprove lists-lookup-under-iff (%cdr-induction xs))
(%autoprove lists-lookup-of-rev-under-iff (%cdr-induction xs))
(%autoprove memberp-of-element-in-lists-lookup (%cdr-induction xs))
(%autoprove memberp-of-in-lists-lookup-in-lists (%cdr-induction xs))
(%deflist none-consp (x)
(consp x)
:negatedp t)
(%deflist disjoint-from-allp (e x)
(disjointp e x))
(%autoprove disjoint-from-allp-when-not-consp-left (%cdr-induction x))
(%autoprove disjoint-from-allp-of-cons-left (%cdr-induction x))
(%autoprove disjoint-from-allp-of-cdr-left)
(%autoprove member-of-nonep-when-memberp-of-disjoint-from-allp (%cdr-induction x))
(%autoprove member-of-nonep-when-memberp-of-disjoint-from-allp-alt)
(%autoprove disjointp-when-memberp-of-disjoint-from-allp-one (%cdr-induction ys))
(%autoprove disjointp-when-memberp-of-disjoint-from-allp-two (%cdr-induction ys))
(%autoprove disjointp-when-memberp-of-disjoint-from-allp-three)
(%autoprove disjointp-when-memberp-of-disjoint-from-allp-four)
(%autoprove disjoint-from-allp-when-subsetp-of-disjoint-from-allp-one (%cdr-induction x))
(%autoprove disjoint-from-allp-when-subsetp-of-disjoint-from-allp-two)
(%autoprove disjoint-from-allp-when-subsetp-of-disjoint-from-allp-three (%cdr-induction ys))
(%autoprove disjoint-from-allp-when-subsetp-of-disjoint-from-allp-four)
(%autoprove disjoint-from-allp-when-memberp (%cdr-induction ys))
(%autoprove disjoint-from-allp-of-list-fix-left)
(%autoprove disjoint-from-allp-of-app-left (%cdr-induction x))
(%autoprove disjoint-from-allp-of-rev-left (%cdr-induction x))
(%autoprove remove-all-when-disjoint-from-allp-and-cons-listp (%cdr-induction x))
(%autoadmit all-disjoint-from-allp)
(%autoprove all-disjoint-from-allp-when-not-consp-one (%restrict default all-disjoint-from-allp (equal xs 'xs)))
(%autoprove all-disjoint-from-allp-of-cons-one (%restrict default all-disjoint-from-allp (equal xs '(cons x xs))))
(%autoprove all-disjoint-from-allp-when-not-consp-two (%cdr-induction xs))
(%autoprove all-disjoint-from-allp-of-cons-two (%cdr-induction xs))
(%autoprove booleanp-of-all-disjoint-from-allp (%cdr-induction xs))
(%autoprove symmetry-of-all-disjoint-from-allp (%cdr-induction xs))
(%autoprove all-disjoint-from-allp-of-list-fix-two (%cdr-induction ys))
(%autoprove all-disjoint-from-allp-of-list-fix-one)
(%autoprove all-disjoint-from-allp-of-app-two (%cdr-induction ys))
(%autoprove all-disjoint-from-allp-of-app-one)
(%autoprove all-disjoint-from-allp-of-rev-two (%cdr-induction ys))
(%autoprove all-disjoint-from-allp-of-rev-one)
(%autoprove all-disjoint-from-allp-when-subsetp-of-other-one (%cdr-induction xs))
(%autoprove all-disjoint-from-allp-when-subsetp-of-other-two)
(%autoprove disjoint-from-allp-when-memberp-of-all-disjoint-from-allp-one (%cdr-induction xs))
(%autoprove disjoint-from-allp-when-memberp-of-all-disjoint-from-allp-two (%cdr-induction ys))
(%autoprove disjointp-when-members-of-all-disjoint-from-allp (%cdr-induction xs))
(%autoprove all-disjoint-from-allp-when-subsetp-of-all-disjoint-one (%cdr-induction xs))
(%autoprove all-disjoint-from-allp-when-subsetp-of-all-disjoint-two)
(%autoprove all-disjoint-from-allp-when-subsetp-of-all-disjoint-three (%cdr-induction ys))
(%autoprove all-disjoint-from-allp-when-subsetp-of-all-disjoint-four)
(%autoadmit mutually-disjointp)
(%autoprove mutually-disjointp-when-not-consp (%restrict default mutually-disjointp (equal xs 'xs)))
(%autoprove mutually-disjointp-of-cons (%restrict default mutually-disjointp (equal xs '(cons x xs))))
(%autoprove booleanp-of-mutually-disjointp (%cdr-induction xs))
(%autoprove mutually-disjointp-of-cdr-when-mutually-disjointp)
(%autoprove mutually-disjointp-of-list-fix (%cdr-induction x))
(%autoprove mutually-disjointp-of-app (%cdr-induction x))
(%autoprove mutually-disjointp-of-rev (%cdr-induction x))
(%autoprove mutually-disjointp-of-remove-all-when-mutually-disjointp (%cdr-induction x))
(%autoprove disjointp-when-both-membersp-of-mutually-disjointp (%cdr-induction xs))
(%autoadmit disjoint-from-allp-badguy)
(defsection disjoint-from-allp-badguy-property
;; BOZO the lemmas need to be unlocalized, and the defthm needs to be added to
;; :rule-classes nil instead of just using defthmd, since it screws up autoprove
;; to have dual conclusions. Actually, do we want to switch this the way that we
;; have done for subsetp-badguy and use the iff rule or whatever?
(%prove (%rule disjoint-from-allp-badguy-property
:hyps (list (%hyp (not (disjoint-from-allp x ys))))
:lhs (and (memberp (disjoint-from-allp-badguy x ys) ys)
(not (disjointp x (disjoint-from-allp-badguy x ys))))
:rhs t))
(%cdr-induction ys)
(%restrict default disjoint-from-allp-badguy (equal ys 'ys))
(%auto)
(%qed))
(%autoprove disjoint-from-allp-of-remove-all-when-memberp-of-mutually-disjointp
(%use (%instance (%thm disjoint-from-allp-badguy-property)
(x x)
(ys (remove-all x xs)))))
(%autoprove member-of-nonep-of-remove-all-when-mutually-disjointp
(%cdr-induction xs))
(%autoprove disjoint-from-allp-when-subsetp-of-remove-all-of-mutually-disjointp)
(%autoprove disjoint-from-allp-when-subsetp-of-remove-all-of-mutually-disjointp-two)
(%autoprove lists-lookup-of-rev-when-mutually-disjointp (%cdr-induction xs))
(%autoprove lists-lookup-when-memberp-in-lists-lookup-when-mutually-disjointp (%cdr-induction xs))
(%autoprove lists-lookup-of-remove-all-from-mutually-disjointp
(%cdr-induction xs))
(%autoprove lists-lookup-when-mutually-disjointp
(%cdr-induction xs))
(%autoprove lists-lookup-of-car-of-lists-lookup
(%use (%instance (%thm lists-lookup-when-mutually-disjointp)
(x (lists-lookup a xs))
(b (car (lists-lookup a xs))))))
(%autoprove member-of-nonep-when-member-of-lists-lookup
(%cdr-induction xs))
(%autoprove member-of-nonep-when-member-of-cdr-of-lists-lookup
(%use (%thm member-of-nonep-when-member-of-lists-lookup)))
(%autoprove member-of-nonep-of-car-of-lists-lookup
(%cdr-induction xs))
(%autoprove member-of-lists-lookup-when-members-of-mutually-disjointp
(%auto)
(%fertilize (lists-lookup a xs) (lists-lookup c xs)))
(%deflist disjoint-from-nonep (e x)
(disjointp e x)
:negatedp t)
(%autoprove disjoint-from-nonep-when-not-consp-left (%cdr-induction x))
(%autoprove disjoint-from-nonep-of-cons-left (%cdr-induction x))
(%autoprove disjoint-from-nonep-of-list-fix-left (%cdr-induction x))
(%autoprove disjoint-from-nonep-of-app-left-one (%cdr-induction x))
(%autoprove disjoint-from-nonep-of-app-left-two (%cdr-induction x))
(%autoprove disjoint-from-nonep-of-rev-left (%cdr-induction x))
(%ensure-exactly-these-rules-are-missing "../../utilities/mutually-disjoint")
|
