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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")
(include-book "remove-duplicates-list")
(%interactive)
(%autoadmit superset-of-somep)
(%autoprove superset-of-somep-when-not-consp (%restrict default superset-of-somep (equal x 'x)))
(%autoprove superset-of-somep-of-cons (%restrict default superset-of-somep (equal x '(cons b x))))
(%autoprove booleanp-of-superset-of-somep (%cdr-induction x))
(%autoprove superset-of-somep-of-list-fix-one (%cdr-induction x))
(%autoprove superset-of-somep-of-list-fix-two (%cdr-induction x))
(%autoprove superset-of-somep-of-app (%cdr-induction x))
(%autoprove superset-of-somep-of-rev (%cdr-induction x))
(%autoprove memberp-when-not-superset-of-somep-cheap (%cdr-induction x))
(%autoprove superset-of-somep-when-obvious (%cdr-induction x))
(%autoprove superset-of-somep-when-obvious-alt)
(%autoadmit find-subset)
(%autoprove find-subset-when-not-consp (%restrict default find-subset (equal x 'x)))
(%autoprove find-subset-of-cons (%restrict default find-subset (equal x '(cons b x))))
(%autoprove find-subset-of-list-fix-one (%cdr-induction x))
(%autoprove find-subset-of-list-fix-two (%cdr-induction x))
(%autoprove find-subset-of-rev-one (%cdr-induction x))
(%autoprove subsetp-of-find-subset (%cdr-induction x))
(%autoprove memberp-of-find-subset (%cdr-induction x))
(%autoprove superset-of-somep-when-find-subset (%cdr-induction x))
(%autoprove find-subset-of-app (%cdr-induction x))
(%autoprove find-subset-when-subsetp-two (%cdr-induction x))
(%autoprove superset-of-somep-when-subsetp-two
(%disable default superset-of-somep-when-obvious superset-of-somep-when-obvious-alt)
(%use (%instance (%thm superset-of-somep-when-obvious)
(a a)
(e (find-subset a x))
(x y))))
(%autoprove superset-of-somep-when-subsetp-two-alt)
(%autoprove superset-of-somep-when-superset-of-somep-of-smaller (%cdr-induction x))
(%autoprove superset-of-somep-when-superset-of-somep-of-smaller-alt (%cdr-induction x))
(%deflist all-superset-of-somep (x ys)
(superset-of-somep x ys))
(%autoprove all-superset-of-somep-of-list-fix-two (%cdr-induction x))
(%autoprove all-superset-of-somep-of-cons-two (%cdr-induction x))
(%autoprove all-superset-of-somep-of-all-two (%cdr-induction x))
(%autoprove all-superset-of-somep-of-all-two-alt (%cdr-induction x))
(%autoprove all-superset-of-somep-of-rev-two (%cdr-induction x))
(%autoprove all-superset-of-somep-when-subsetp-two (%cdr-induction x))
(%autoprove all-superset-of-somep-when-subsetp-two-alt (%cdr-induction x))
(%autoprove all-superset-of-somep-of-cons-two-when-irrelevant (%cdr-induction x))
(%autoprove all-superset-of-somep-of-app-two-when-irrelevant (%cdr-induction y))
(%autoprove superset-of-somep-when-all-superset-of-somep (%cdr-induction x))
(%autoprove superset-of-somep-when-all-superset-of-somep-alt)
(%autoprove all-superset-of-somep-is-reflexive (%cdr-induction x))
(%autoprove all-superset-of-somep-is-transitive (%cdr-induction x))
(%autoprove all-superset-of-somep-of-remove-duplicates-list (%cdr-induction x))
(%autoprove all-superset-of-somep-of-remove-duplicates-list-gen (%cdr-induction x))
(%autoadmit remove-supersets1)
(%autoprove remove-supersets1-when-not-consp (%restrict default remove-supersets1 (equal todo 'x)))
(%autoprove remove-supersets1-of-cons (%restrict default remove-supersets1 (equal todo '(cons a x))))
(%autoprove true-listp-of-remove-supersets1 (%autoinduct remove-supersets1 x done))
(%autoprove uniquep-of-remove-supersets1 (%autoinduct remove-supersets1 todo done))
(%autoprove all-superset-of-somep-of-remove-supersets1 (%autoinduct remove-supersets1 todo done))
(%autoprove cons-listp-when-not-superset-of-some-is-non-consp (%cdr-induction x))
(%autoprove cons-listp-of-remove-supersets1 (%autoinduct remove-supersets1 todo done))
(%autoadmit remove-supersets)
(%autoprove true-listp-of-remove-supersets (%enable default remove-supersets))
(%autoprove all-superset-of-somep-of-remove-supersets (%enable default remove-supersets))
(%autoprove all-superset-of-somep-of-remove-supersets-gen (%enable default remove-supersets))
(%autoprove cons-listp-of-remove-supersets (%enable default remove-supersets))
(%autoadmit subset-of-somep)
(%autoprove subset-of-somep-when-not-consp (%restrict default subset-of-somep (equal x 'x)))
(%autoprove subset-of-somep-of-cons (%restrict default subset-of-somep (equal x '(cons b x))))
(%autoprove booleanp-of-subset-of-somep (%cdr-induction x))
(%autoprove subset-of-somep-of-list-fix-one (%cdr-induction x))
(%autoprove subset-of-somep-of-list-fix-two (%cdr-induction x))
(%autoprove subset-of-somep-of-app (%cdr-induction x))
(%autoprove subset-of-somep-of-rev (%cdr-induction x))
(%autoprove memberp-when-not-subset-of-somep-cheap (%cdr-induction x))
(%autoprove subset-of-somep-when-obvious (%cdr-induction x))
(%autoprove subset-of-somep-when-obvious-alt)
(%autoadmit find-superset)
(%autoprove find-superset-when-not-consp (%restrict default find-superset (equal x 'x)))
(%autoprove find-superset-of-cons (%restrict default find-superset (equal x '(cons b x))))
(%autoprove find-superset-of-list-fix-one (%cdr-induction x))
(%autoprove find-superset-of-list-fix-two (%cdr-induction x))
(%autoprove find-superset-of-rev-one (%cdr-induction x))
(%autoprove subsetp-of-find-superset (%cdr-induction x))
(%autoprove memberp-of-find-superset (%cdr-induction x))
(%autoprove subset-of-somep-when-find-superset (%cdr-induction x))
(%autoprove find-superset-when-subsetp-two (%cdr-induction x))
(%autoprove subset-of-somep-when-subsetp-two
(%disable default subset-of-somep-when-obvious subset-of-somep-when-obvious-alt)
(%use (%instance (%thm subset-of-somep-when-obvious)
(a a)
(e (find-superset a x))
(x y))))
(%autoprove subset-of-somep-when-subsetp-two-alt)
(%autoprove subset-of-somep-when-subset-of-somep-of-smaller (%cdr-induction x))
(%autoprove subset-of-somep-when-subset-of-somep-of-smaller-alt (%cdr-induction x))
(%deflist all-subset-of-somep (x ys)
(subset-of-somep x ys))
(%autoprove all-subset-of-somep-of-list-fix-two (%cdr-induction x))
(%autoprove all-subset-of-somep-of-cons-two (%cdr-induction x))
(%autoprove all-subset-of-somep-of-all-two (%cdr-induction x))
(%autoprove all-subset-of-somep-of-all-two-alt (%cdr-induction x))
(%autoprove all-subset-of-somep-of-rev-two (%cdr-induction x))
(%autoprove all-subset-of-somep-when-subsetp-two (%cdr-induction x))
(%autoprove all-subset-of-somep-when-subsetp-two-alt (%cdr-induction x))
(%autoprove all-subset-of-somep-of-cons-two-when-irrelevant (%cdr-induction x))
(%autoprove all-subset-of-somep-of-app-two-when-irrelevant (%cdr-induction y))
(%autoprove subset-of-somep-when-all-subset-of-somep (%cdr-induction x))
(%autoprove subset-of-somep-when-all-subset-of-somep-alt)
(%autoprove all-subset-of-somep-is-reflexive (%cdr-induction x))
(%autoprove all-subset-of-somep-is-transitive (%cdr-induction x))
(%autoprove all-subset-of-somep-of-remove-duplicates-list (%cdr-induction x))
(%autoprove all-subset-of-somep-of-remove-duplicates-list-gen (%cdr-induction x))
(%ensure-exactly-these-rules-are-missing "../../utilities/extended-subsets")
|
