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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-4-remove-all")
(include-book "utilities-4-disjointp")
(include-book "utilities-4-uniquep")
(include-book "utilities-4-difference")
(include-book "utilities-4-remove-duplicates")
(include-book "utilities-4-tuplep")
(include-book "utilities-4-repeat")
(include-book "utilities-4-nth")
(%interactive)
;; Extra theorems for disjointp.
(%autoprove disjointp-of-remove-all-of-remove-all-when-disjointp-right)
(%autoprove disjointp-of-remove-all-when-disjointp-left)
;; Extra theorems for uniquep.
(%autoprove uniquep-of-app
(%cdr-induction x))
(%autoprove uniquep-of-rev
(%cdr-induction x))
(%autoprove uniquep-of-remove-all-when-uniquep
(%cdr-induction x))
;; Extra theorems for difference.
(%autoprove uniquep-of-difference-when-uniquep
(%cdr-induction x))
(%autoprove disjointp-of-difference-with-y
(%cdr-induction x))
(%autoprove disjointp-of-difference-with-y-alt
(%cdr-induction x))
;; Extra theorems for remove-duplicates.
(%autoprove uniquep-of-remove-duplicates
(%cdr-induction x))
(%autoprove remove-duplicates-of-difference
(%cdr-induction x))
(%autoprove remove-duplicates-when-unique
(%cdr-induction x))
(%autoprove app-of-remove-duplicates-with-unique-and-disjoint
(%cdr-induction x))
(%autoprove remove-duplicates-of-remove-all
(%cdr-induction x))
(%autoprove subsetp-of-remove-all-of-remove-duplicates)
;; Extra theorems for nth.
(%autoprove equal-of-nths-when-uniquep
;; This proof is pretty cool. It has really improved over time as my
;; tactics have gotten better.
(%induct (rank x)
((not (consp x))
nil)
((and (consp x)
(or (zp m)
(zp n)))
nil)
((and (consp x)
(not (zp m))
(not (zp n)))
(((x (cdr x))
(n (- n 1))
(m (- m 1))))))
(%restrict default nth (or (equal n 'n) (equal n 'm) (equal n ''0) (equal n ''1))))
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