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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")
(%interactive)
(%autoadmit firstn)
(%autoprove firstn-of-zero
(%restrict default firstn (equal n ''0)))
(%autoprove true-listp-of-firstn
(%autoinduct firstn)
(%restrict default firstn (equal n 'n)))
(%autoprove consp-of-firstn
(%autoinduct firstn)
(%restrict default firstn (or (equal n 'n) (equal n ''1))))
(%autoprove firstn-under-iff
(%restrict default firstn (equal n 'n)))
(%autoprove firstn-of-list-fix
(%autoinduct firstn)
(%restrict default firstn (equal n 'n)))
(%autoprove firstn-of-len
(%cdr-induction x)
(%restrict default firstn (equal n '(+ '1 (len x2)))))
(%autoprove len-of-firstn
(%autoinduct firstn)
(%restrict default firstn (or (equal n 'n) (equal n ''1))))
(%autoprove firstn-of-too-many
(%autoinduct firstn)
(%restrict default firstn (equal n 'n)))
(defsection firstn-of-too-many-replacement
;; BOZO fix acl2 to limit this
;; -- NO, wait! First check if we need to do that now that we
;; have our cache working
(%prove (%rule firstn-of-too-many-replacement
:hyps (list (%hyp (< (len x) n) :limit 1))
:lhs (firstn n x)
:rhs (list-fix x)))
(%auto)
(%qed)
(%disable default firstn-of-too-many)
(%enable default firstn-of-too-many-replacement))
(%autoprove firstn-of-app
;; BOZO check if we still need this disable with our cache
(%autoinduct firstn)
(%disable default len-when-tuplep trichotomy-of-< antisymmetry-of-<)
(%restrict default firstn (equal n 'n)))
(%autoprove subsetp-of-firstn-when-in-range
(%autoinduct firstn)
(%restrict default firstn (equal n 'n)))
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