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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")
(%interactive)
;; BOZO move these to utilities or wherever max is defined
(defthm max-of-nfix-left
(equal (max (nfix a) b)
(max a b)))
(defthm max-of-nfix-right
(equal (max a (nfix b))
(max a b)))
(%autoprove max-of-nfix-left)
(%autoprove max-of-nfix-right)
(%autoadmit clause.flag-depth)
(%autoadmit clause.depth)
(%autoadmit clause.depth-list)
(%autoprove definition-of-clause.depth
(%restrict default clause.flag-depth (equal x 'x))
(%enable default clause.depth clause.depth-list))
(%autoprove definition-of-clause.depth-list
(%restrict default clause.flag-depth (equal x 'x))
(%enable default clause.depth clause.depth-list))
(%autoprove clause.flag-depth-of-term
(%enable default clause.depth))
(%autoprove clause.flag-depth-of-list
(%enable default clause.depth-list))
(%autoprove forcing-clause.depth-of-logic.function
(%restrict default definition-of-clause.depth (memberp x '((logic.function fn args)
(logic.function 'if args))))
(%forcingp nil))
(%autoprove forcing-clause.depth-of-logic.lambda
(%restrict default definition-of-clause.depth (equal x '(logic.lambda formals body actuals)))
(%forcingp nil))
(%autoprove clause.depth-list-when-not-consp
(%restrict default definition-of-clause.depth-list (equal x 'x)))
(%autoprove clause.depth-list-of-cons
(%restrict default definition-of-clause.depth-list (equal x '(cons a x))))
(%autoprove clause.depth-list-when-length-three
(%disable default max))
(%autoprove lemma-for-natp-of-clause.depth
(%clause.simple-term-induction flag x)
(%restrict default definition-of-clause.depth (equal x 'x)))
(%autoprove natp-of-clause.depth
(%use (%instance (%thm lemma-for-natp-of-clause.depth) (flag 'term))))
(%autoprove natp-of-clause.depth-list
(%use (%instance (%thm lemma-for-natp-of-clause.depth) (flag 'list))))
(%autoprove clause.depth-list-of-list-fix
(%cdr-induction x))
(%autoprove clause.depth-list-of-app
(%cdr-induction x))
(%autoprove clause.depth-list-of-rev
(%cdr-induction x))
(%autoprove lemma-for-clause.depth-zero
(%clause.simple-term-induction flag x)
(%restrict default definition-of-clause.depth (equal x 'x)))
(%autoprove clause.depth-zero
(%use (%instance (%thm lemma-for-clause.depth-zero) (flag 'term))))
(%autoprove clause.depth-list-zero
(%use (%instance (%thm lemma-for-clause.depth-zero) (flag 'list))))
(%autoprove clause.depth-when-clause.simple-termp)
(%autoprove clause.depth-list-when-clause.simple-term-listp)
(%autoprove clause.depth-positive-when-non-clause.simple-termp)
(%autoprove clause.depth-list-positive-when-non-clause.simple-term-listp)
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