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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 "mergesort")
(%interactive)
(%autoadmit ordered-mapp)
(%autoprove ordered-mapp-when-not-consp
(%restrict default ordered-mapp (equal x 'x)))
(%autoprove ordered-mapp-when-not-consp-of-cdr
(%restrict default ordered-mapp (equal x 'x)))
(%autoprove ordered-mapp-of-cons
(%restrict default ordered-mapp (equal x '(cons a x))))
(%autoprove booleanp-of-ordered-mapp
(%cdr-induction x))
(%autoprove ordered-mapp-of-cdr-when-ordered-mapp)
(%autoprove lemma-for-uniquep-when-ordered-mapp
(%cdr-induction x))
(%autoprove uniquep-of-domain-when-ordered-mapp
(%cdr-induction x)
(%enable default lemma-for-uniquep-when-ordered-mapp))
(%autoadmit merge-maps)
(%autoprove merge-maps-when-not-consp-left
(%restrict default merge-maps (and (equal x 'x) (equal y 'y))))
(%autoprove merge-maps-when-not-consp-right
(%restrict default merge-maps (and (equal x 'x) (equal y 'y))))
(%autoprove merge-maps-of-cons-and-cons
(%restrict default merge-maps (and (or (equal x '(cons a x))
(equal x '(cons b x)))
(or (equal y '(cons a y))
(equal y '(cons b y))))))
(%autoprove consp-of-merge-maps
(%restrict default merge-maps (and (equal x 'x) (equal y 'y))))
(%autoprove lookup-of-first-of-first)
(%autoprove lookup-when-not-first-of-first)
(%autoprove smaller-than-merge-maps
(%autoinduct merge-maps)
(%restrict default merge-maps (and (equal x 'x) (equal y 'y))))
(%autoprove ordered-mapp-of-merge-maps
(%autoinduct merge-maps x y)
(%restrict default merge-maps (and (equal x 'x) (equal y 'y))))
(%autoprove mapp-of-merge-maps
(%autoinduct merge-maps x y)
(%restrict default merge-maps (and (equal x 'x) (equal y 'y))))
(%autoprove lookup-of-merge-maps
(%autoinduct merge-maps x y)
(%restrict default merge-maps (and (equal x 'x) (equal y 'y)))
(%enable default
lemma-2-for-ordered-list-subsetp-property
lemma-for-uniquep-when-ordered-mapp))
(%autoadmit mergesort-map)
(%autoprove mergesort-map-when-not-consp
(%restrict default mergesort-map (equal x 'x)))
(%autoprove mergesort-map-when-not-consp-of-cdr
(%restrict default mergesort-map (equal x 'x)))
(%autoprove mapp-of-mergesort-map
(%autoinduct mergesort-map)
(%restrict default mergesort-map (equal x 'x)))
(%autoprove ordered-mapp-of-mergesort-map
(%autoinduct mergesort-map)
(%restrict default mergesort-map (equal x 'x)))
(verify-guards mergesort-map)
(%autoprove uniquep-of-domain-of-mergesort-map)
(%autoprove lemma-1-for-lookup-of-mergesort-map
(%use (%instance (%thm halve-list-lookup-property))))
(%autoprove lemma-2-for-lookup-of-mergesort-map
(%use (%instance (%thm halve-list-lookup-property))))
(%autoprove lookup-of-mergesort-map
(%autoinduct mergesort-map)
(%restrict default mergesort-map (equal x 'x))
(%enable default lemma-1-for-lookup-of-mergesort-map
lemma-2-for-lookup-of-mergesort-map))
(%autoprove submapp-of-mergesort-map-and-self-left
(%use (%instance (%thm submapp-badguy-membership-property)
(x (mergesort-map x))
(y x))))
(%autoprove submapp-of-mergesort-map-and-self-right
(%use (%instance (%thm submapp-badguy-membership-property)
(y (mergesort-map x))
(x x))))
(%autoprove submapp-of-mergesort-map-left)
(%autoprove submapp-of-mergesort-map-right)
(%autoadmit ordered-map-submapp)
(%autoprove ordered-map-submapp-when-not-consp-left
(%restrict default ordered-map-submapp (and (equal x 'x) (equal y 'y))))
(%autoprove ordered-map-submapp-when-not-consp-right
(%restrict default ordered-map-submapp (and (equal x 'x) (equal y 'y))))
(%autoprove ordered-map-submapp-of-cons-and-cons
(%restrict default ordered-map-submapp (and (or (equal x '(cons a x))
(equal x '(cons b x)))
(or (equal y '(cons a y))
(equal y '(cons b y))))))
(%autoprove booleanp-of-ordered-map-submapp
(%autoinduct ordered-map-submapp x y))
(%autoprove lemma-1-for-ordered-map-submapp-property)
(%autoprove lemma-2-for-ordered-map-submapp-property
(%enable default submapp))
(%autoprove lemma-3-for-ordered-map-submapp-property
(%disable default equal-of-lookups-when-submapp)
(%use (%instance (%thm equal-of-lookups-when-submapp)
(x x)
(y y)
(a (car (car x))))))
(%autoprove lemma-4-for-ordered-map-submapp-property-aux
(%autoinduct submapp1 dom x y)
(%restrict default submapp1 (equal domain 'dom)))
(%autoprove lemma-4-for-ordered-map-submapp-property
(%enable default
lemma-4-for-ordered-map-submapp-property-aux
lemma-for-uniquep-when-ordered-mapp
submapp))
(%autoprove lemma-5-for-ordered-map-submapp-property
(%disable default lemma-for-uniquep-when-ordered-mapp)
(%use (%instance (%thm lemma-for-uniquep-when-ordered-mapp)
(a (first (first x)))
(x y))))
(%autoprove lemma-6-for-ordered-map-submapp-property
(%disable default equal-of-lookups-when-submapp)
(%use (%instance (%thm equal-of-lookups-when-submapp)
(a (first (first x)))
(x x)
(y y)))
(%auto :strategy (cleanup split urewrite crewrite))
(%restrict default lookup (or (equal x 'x) (equal y 'y))))
(%autoprove lemma-7-for-ordered-map-submapp-property-aux
(%autoinduct submapp1 dom x y)
(%restrict default submapp1 (equal domain 'dom)))
(%autoprove lemma-7-for-ordered-map-submapp-property
(%enable default
submapp
lemma-for-uniquep-when-ordered-mapp)
(%use (%instance (%thm lemma-7-for-ordered-map-submapp-property-aux)
(dom (domain x)))))
(%autoprove ordered-map-submapp-property
(%autoinduct ordered-map-submapp x y)
(%enable default lemma-for-uniquep-when-ordered-mapp
lemma-1-for-ordered-map-submapp-property
lemma-2-for-ordered-map-submapp-property
lemma-3-for-ordered-map-submapp-property
lemma-4-for-ordered-map-submapp-property
lemma-5-for-ordered-map-submapp-property
lemma-6-for-ordered-map-submapp-property
lemma-7-for-ordered-map-submapp-property))
(%autoprove lemma-for-ordered-listp-when-ordered-mapp
(%restrict default << (and (equal x 'a) (equal y 'b))))
(%autoprove ordered-listp-when-ordered-mapp
(%cdr-induction x)
(%enable default lemma-for-ordered-listp-when-ordered-mapp))
(%autoprove ordered-listp-of-mergesort-map)
(%ensure-exactly-these-rules-are-missing "../../../utilities/mergesort")
|
