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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 "primary-eqtrace")
(include-book "secondary-eqtrace")
(include-book "transitivity-eqtraces")
(include-book "weakening-eqtrace")
(include-book "direct-iff-eqtrace")
(include-book "negative-iff-eqtrace")
(%interactive)
(%autoadmit rw.eqtrace-step-okp)
(%autoprove booleanp-of-rw.eqtrace-step-okp
(%enable default rw.eqtrace-step-okp))
(%autoadmit rw.flag-eqtrace-okp)
(%autoadmit rw.eqtrace-okp)
(%autoadmit rw.eqtrace-list-okp)
(%autoprove definition-of-rw.eqtrace-okp
(%restrict default rw.flag-eqtrace-okp (equal x 'x))
(%enable default rw.eqtrace-okp rw.eqtrace-list-okp))
(%autoprove definition-of-rw.eqtrace-list-okp
(%restrict default rw.flag-eqtrace-okp (equal x 'x))
(%enable default rw.eqtrace-okp rw.eqtrace-list-okp))
(%autoprove rw.flag-eqtrace-okp-of-trace
(%enable default rw.eqtrace-okp))
(%autoprove rw.flag-eqtrace-okp-of-list
(%enable default rw.eqtrace-list-okp))
(%autoprove lemma-for-booleanp-of-rw.eqtrace-okp
(%rw.flag-eqtracep-induction flag x)
(%restrict default definition-of-rw.eqtrace-okp (equal x 'x))
(%restrict default definition-of-rw.eqtrace-list-okp (equal x 'x)))
(%autoprove booleanp-of-rw.eqtrace-okp
(%use (%instance (%thm lemma-for-booleanp-of-rw.eqtrace-okp)
(flag 'trace))))
(%autoprove booleanp-of-rw.eqtrace-list-okp
(%use (%instance (%thm lemma-for-booleanp-of-rw.eqtrace-okp)
(flag 'list))))
(%autoprove rw.eqtrace-list-okp-when-not-consp
(%restrict default definition-of-rw.eqtrace-list-okp (equal x 'x)))
(%autoprove rw.eqtrace-list-okp-of-cons
(%restrict default definition-of-rw.eqtrace-list-okp (equal x '(cons a x))))
(%autoprove rw.eqtrace-step-okp-of-nil
(%enable default rw.eqtrace-step-okp))
(%autoprove rw.eqtrace-okp-of-nil
(%restrict default definition-of-rw.eqtrace-okp (equal x ''nil)))
(%deflist rw.eqtrace-list-okp (x box)
(rw.eqtrace-okp x box))
(%autoprove forcing-rw.eqtrace-list-okp-of-rw.eqtrace-subtraces
(%restrict default definition-of-rw.eqtrace-okp (equal x 'x)))
(%autoprove rw.primary-eqtrace-okp-when-empty-box
(%enable default rw.primary-eqtrace-okp))
(%autoprove rw.secondary-eqtrace-okp-when-empty-box
(%enable default rw.secondary-eqtrace-okp))
(%autoprove lemma-for-rw.eqtrace-okp-when-empty-box
(%rw.flag-eqtracep-induction flag x)
(%restrict default definition-of-rw.eqtrace-okp (equal x 'x))
(%auto)
(%forcingp nil)
(%enable default
rw.eqtrace-step-okp
rw.trans1-eqtrace-okp
rw.trans2-eqtrace-okp
rw.trans3-eqtrace-okp
rw.weakening-eqtrace-okp
rw.direct-iff-eqtrace-okp
rw.negative-iff-eqtrace-okp))
(%autoprove rw.eqtrace-okp-when-empty-box
(%use (%instance (%thm lemma-for-rw.eqtrace-okp-when-empty-box)
(flag 'trace))))
(%autoprove rw.eqtrace-list-okp-when-empty-box
(%use (%instance (%thm lemma-for-rw.eqtrace-okp-when-empty-box)
(flag 'list))))
(encapsulate
()
(local (%enable default rw.eqtrace-step-okp))
(%autoprove forcing-rw.eqtrace-okp-of-rw.primary-eqtrace
(%restrict default definition-of-rw.eqtrace-okp
(memberp x '((rw.primary-eqtrace okp nhyp)
(rw.primary-eqtrace 't nhyp)))))
(%autoprove forcing-rw.eqtrace-okp-of-rw.secondary-eqtrace
(%restrict default definition-of-rw.eqtrace-okp
(memberp x '((rw.secondary-eqtrace okp nhyp)
(rw.secondary-eqtrace 't nhyp)))))
(%autoprove forcing-rw.eqtrace-okp-of-rw.trans1-eqtrace
(%restrict default definition-of-rw.eqtrace-okp (equal x '(rw.trans1-eqtrace iffp x y))))
(%autoprove forcing-rw.eqtrace-okp-of-rw.trans2-eqtrace
(%restrict default definition-of-rw.eqtrace-okp (equal x '(rw.trans2-eqtrace iffp x y))))
(%autoprove forcing-rw.eqtrace-okp-of-rw.trans3-eqtrace
(%restrict default definition-of-rw.eqtrace-okp (equal x '(rw.trans3-eqtrace iffp x y))))
(%autoprove forcing-rw.eqtrace-okp-of-rw.weakening-eqtrace
(%restrict default definition-of-rw.eqtrace-okp (equal x '(rw.weakening-eqtrace x))))
(%autoprove forcing-rw.eqtrace-okp-of-rw.direct-iff-eqtrace
(%restrict default definition-of-rw.eqtrace-okp
(memberp x '((rw.direct-iff-eqtrace okp nhyp)
(rw.direct-iff-eqtrace 't nhyp)))))
(%autoprove forcing-rw.eqtrace-okp-of-rw.negative-iff-eqtrace
(%restrict default definition-of-rw.eqtrace-okp
(memberp x '((rw.negative-iff-eqtrace okp nhyp)
(rw.negative-iff-eqtrace 't nhyp))))))
(%autoadmit rw.eqtrace-formula)
(%autoprove forcing-logic.formulap-of-rw.eqtrace-formula
(%enable default rw.eqtrace-formula))
(%autoprove forcing-logic.formula-atblp-of-rw.eqtrace-formula
(%enable default rw.eqtrace-formula))
(%defprojection :list (rw.eqtrace-formula-list x box)
:element (rw.eqtrace-formula x box))
(%autoprove forcing-logic.formula-listp-of-rw.eqtrace-formula-list
(%cdr-induction x))
(%autoprove forcing-logic.formula-list-atblp-of-rw.eqtrace-formula
(%cdr-induction x))
(%ensure-exactly-these-rules-are-missing "../../rewrite/assms/eqtrace-okp")
|
