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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-5")
(%interactive)
(%autoadmit submapp1)
(%autoprove submapp1-when-not-consp
(%restrict default submapp1 (equal domain 'domain)))
(%autoprove submapp1-of-cons
(%restrict default submapp1 (equal domain '(cons a domain))))
(%autoprove booleanp-of-submapp1
(%cdr-induction domain))
(%autoprove equal-of-lookups-when-memberp-of-submapp1-domain
(%cdr-induction domain))
(%autoprove lookup-when-memberp-of-submapp1
(%use (%instance (%thm equal-of-lookups-when-memberp-of-submapp1-domain))))
(%autoadmit submapp1-badguy)
(%autoprove submapp1-badguy-when-not-consp
(%restrict default submapp1-badguy (equal domain 'domain)))
(%autoprove submapp1-badguy-of-cons
(%restrict default submapp1-badguy (equal domain '(cons a domain))))
(%autoprove submapp1-badguy-membership-property
(%cdr-induction domain)
(%enable default submapp1-badguy-when-not-consp submapp1-badguy-of-cons))
(%autoprove submapp1-badguy-under-iff
(%cdr-induction domain)
(%enable default submapp1-badguy-when-not-consp submapp1-badguy-of-cons))
(%autoprove submapp1-when-submapp1-of-domain-superset-one
(%use (%instance (%thm submapp1-badguy-membership-property) (domain domain1) (x x) (y y))))
(%autoprove submapp1-when-submapp1-of-domain-superset-two
(%use (%instance (%thm submapp1-when-submapp1-of-domain-superset-one))))
(%autoprove submapp1-of-list-fix-one)
(%autoprove submapp1-of-list-fix-two
(%cdr-induction domain))
(%autoprove submapp1-of-list-fix-three
(%cdr-induction domain))
(%autoadmit submapp)
(%autoprove booleanp-of-submapp
(%enable default submapp))
(%autoprove submapp-of-list-fix-one
(%enable default submapp))
(%autoprove submapp-of-list-fix-two
(%enable default submapp))
(%autoprove equal-of-lookups-when-submapp
(%enable default submapp))
(%autoprove equal-of-cdrs-of-lookups-when-submapp
(%disable default equal-of-lookups-when-submapp)
(%use (%instance (%thm equal-of-lookups-when-submapp))))
(%autoprove lookup-when-lookup-in-submapp-one
(%enable default submapp))
(%autoprove lookup-when-lookup-in-submapp-two
(%use (%instance (%thm lookup-when-lookup-in-submapp-one))))
(%autoadmit submapp-badguy)
(%autoprove submapp-badguy-membership-property
(%enable default submapp-badguy)
(%use (%instance (%thm submapp1-badguy-membership-property)
(domain (domain x)))))
(%autoprove submapp-badguy-under-iff
(%enable default submapp submapp-badguy))
(%autoprove subsetp-of-domains-when-submap
(%use (%instance (%thm subsetp-badguy-membership-property) (x (domain x)) (y (domain y)))))
(%autoprove submapp-reflexive
(%use (%instance (%thm submapp-badguy-membership-property) (x x) (y x))))
(%autoprove submapp-transitive
(%use (%instance (%thm submapp-badguy-membership-property) (x x) (y z)))
(%waterfall default 40)
(%disable default equal-of-lookups-when-submapp)
(%use (%instance (%thm equal-of-lookups-when-submapp) (a (cdr (submapp-badguy x z))) (x x) (y y)))
(%use (%instance (%thm equal-of-lookups-when-submapp) (a (cdr (submapp-badguy x z))) (x y) (y z)))
(%waterfall default 40))
(%autoprove submapp-transitive-alt)
(%autoprove lemma-for-submapp1-of-app
(%use (%instance (%thm submapp1-badguy-membership-property) (domain (app d1 d2)) (x a) (y b))))
(%autoprove submapp1-of-app
(%enable default lemma-for-submapp1-of-app))
(%autoprove lemma-for-submapp-of-cons-onto-map
(%cdr-induction x))
(%autoprove submapp-of-cons-onto-map
(%cdr-induction map)
(%enable default lemma-for-submapp-of-cons-onto-map submapp))
(%autoprove lemma-for-submapp-when-unique-domains-and-subsetp
(%cdr-induction x))
(%autoprove lemma2-for-submapp-when-unique-domains-and-subsetp
(%enable default lemma-for-submapp-when-unique-domains-and-subsetp)
(%cdr-induction x))
(%autoprove submapp-when-unique-domains-and-subsetp
(%enable default lemma2-for-submapp-when-unique-domains-and-subsetp)
(%use (%instance (%thm submapp-badguy-membership-property) (x x) (y y))))
(%autoprove lemma-for-submapp-of-app-when-submapp
(%cdr-induction dom))
(%autoprove submapp-of-app-when-submapp
(%enable default submapp lemma-for-submapp-of-app-when-submapp))
(%autoprove submapp-of-rev-when-uniquep
(%enable default domain-of-rev)
(%disable default [outside]rev-of-domain rev-of-domain))
|
