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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 "casesplit")
(%interactive)
(%autoprove cdr-of-logic.smart-negate-formulas)
(%autoprove car-of-logic.smart-negate-formulas
(%forcingp nil))
(%autoadmit clause.cases-bldr)
(defthm lemma-for-forcing-logic.appealp-of-clause.cases-bldr-alt
;; BOZO the real lemma needs :rule-classes nil added
(implies (and (logic.termp a)
(logic.term-listp cases)
(logic.term-listp (domain assignment)))
(and (logic.appealp (clause.cases-bldr a cases assignment))
(equal (logic.conclusion (clause.cases-bldr a cases assignment))
(if (consp assignment)
(logic.por (logic.disjoin-formulas (logic.smart-negate-formulas (assignment-formulas assignment)))
(logic.pequal a (clause.casesplit a cases assignment)))
(logic.pequal a (clause.casesplit a cases assignment))))))
:rule-classes nil)
(%autoprove lemma-for-forcing-logic.appealp-of-clause.cases-bldr-alt
(%clause.cases-induction cases assignment)
(%disable default
expensive-arithmetic-rules
expensive-arithmetic-rules-two
expensive-term/formula-inference
type-set-like-rules
forcing-logic.function-of-logic.function-name-and-logic.function-args-free)
(%auto :strategy (cleanup split))
(%restrict default clause.cases-bldr (equal cases 'cases))
(%restrict default clause.casesplit (equal cases 'cases)))
(%autoprove forcing-logic.appealp-of-clause.cases-bldr
(%use (%instance (%thm lemma-for-forcing-logic.appealp-of-clause.cases-bldr-alt))))
(%autoprove forcing-logic.conclusion-of-clause.cases-bldr
(%use (%instance (%thm lemma-for-forcing-logic.appealp-of-clause.cases-bldr-alt))))
(%autoprove forcing-proofp-of-clause.cases-bldr
(%clause.cases-induction cases assignment)
(%disable default
expensive-arithmetic-rules
expensive-arithmetic-rules-two
expensive-term/formula-inference
type-set-like-rules
forcing-logic.function-of-logic.function-name-and-logic.function-args-free)
(%auto :strategy (cleanup split))
(%restrict default clause.cases-bldr (equal cases 'cases))
(%restrict default clause.casesplit (equal cases 'cases)))
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