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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 "clause-basics")
(%interactive)
(local (%enable default
bust-up-logic.function-args-expensive
bust-up-cdr-of-logic.function-args-expensive
bust-up-cdr-of-cdr-of-logic.function-args-expensive))
(defsection clause.obvious-termp
(%autoadmit clause.obvious-termp)
(%autoprove booleanp-of-clause.obvious-termp
(%enable default clause.obvious-termp)))
(defsection clause.obvious-term-bldr
(%autoadmit clause.obvious-term-bldr)
(local (%enable default
clause.obvious-term-bldr
clause.obvious-termp
clause.negative-termp
clause.negative-term-guts
logic.term-formula
theorem-if-redux-nil
definition-of-not))
(%autoprove clause.obvious-term-bldr-under-iff)
(%autoprove forcing-logic.appealp-of-clause.obvious-term-bldr)
(%autoprove forcing-logic.conclusion-of-clause.obvious-term-bldr)
(%autoprove forcing-logic.proofp-of-clause.obvious-term-bldr
(%disable default forcing-lookup-of-logic.function-name-free)))
(defsection clause.find-obvious-term
(%autoadmit clause.find-obvious-term)
(%autoprove clause.find-obvious-term-when-not-consp
(%restrict default clause.find-obvious-term (equal x 'x)))
(%autoprove clause.find-obvious-term-of-cons
(%restrict default clause.find-obvious-term (equal x '(cons a x))))
(%autoprove clause.find-obvious-term-of-list-fix
(%cdr-induction x))
(%autoprove clause.find-obvious-term-of-app
(%cdr-induction x))
(%autoprove clause.find-obvious-term-of-rev-under-iff
(%cdr-induction x))
(%autoprove forcing-memberp-of-clause.find-obvious-term
(%cdr-induction x))
(%autoprove logic.termp-of-clause.find-obvious-term
(%cdr-induction x))
(%autoprove clause.obvious-termp-of-clause.find-obvious-term
(%cdr-induction x)))
(defsection clause.remove-obvious-clauses
(%autoadmit clause.remove-obvious-clauses)
(%autoprove clause.remove-obvious-clauses-when-not-consp
(%restrict default clause.remove-obvious-clauses (equal x 'x)))
(%autoprove clause.remove-obvious-clauses-of-cons
(%restrict default clause.remove-obvious-clauses (equal x '(cons a x))))
(%autoprove true-listp-of-clause.remove-obvious-clauses
(%cdr-induction x))
(%autoprove clause.remove-obvious-clauses-of-list-fix
(%cdr-induction x))
(%autoprove clause.remove-obvious-clauses-of-app
(%cdr-induction x))
(%autoprove rev-of-clause.remove-obvious-clauses
(%cdr-induction x))
(%autoprove clause.remove-obvious-clauses-of-rev)
(%autoprove subsetp-of-clause.remove-obvious-clauses
(%cdr-induction x))
(%autoprove forcing-logic.term-list-listp-of-clause.remove-obvious-clauses
(%cdr-induction x))
(%autoprove forcing-logic.term-list-list-atblp-of-clause.remove-obvious-clauses
(%cdr-induction x))
(%autoprove cons-listp-of-clause.remove-obvious-clauses
(%cdr-induction x))
(%autoprove all-superset-of-somep-of-clause.remove-obvious-clauses
(%cdr-induction x)))
(defsection clause.remove-obvious-clauses-bldr
(%autoadmit clause.remove-obvious-clauses-bldr)
(local (%restrict default clause.remove-obvious-clauses-bldr (equal x 'x)))
(%autoprove forcing-logic.appeal-listp-of-clause.remove-obvious-clauses-bldr
(%autoinduct clause.remove-obvious-clauses-bldr))
(%autoprove forcing-logic.strip-conclusions-of-clause.remove-obvious-clauses-bldr
(%autoinduct clause.remove-obvious-clauses-bldr))
(%autoprove forcing-logic.proof-listp-of-clause.remove-obvious-clauses-bldr
(%autoinduct clause.remove-obvious-clauses-bldr)))
(defsection clause.obvious-term-bldr-okp
(%autoadmit clause.obvious-term-bldr-okp)
(local (%enable default clause.obvious-term-bldr-okp logic.term-formula))
(%autoprove booleanp-of-clause.obvious-term-bldr-okp)
(%autoprove clause.obvious-term-bldr-okp-of-logic.appeal-identity)
(local (%enable default backtracking-logic.formula-atblp-rules))
(local (%disable default
forcing-logic.formula-atblp-rules
forcing-lookup-of-logic.function-name-free))
(%autoprove lemma-1-for-soundness-of-clause.obvious-term-bldr-okp)
(%autoprove lemma-2-for-soundness-of-clause.obvious-term-bldr-okp)
(%autoprove forcing-soundness-of-clause.obvious-term-bldr-okp
(%use (%instance (%thm lemma-1-for-soundness-of-clause.obvious-term-bldr-okp)))
(%use (%instance (%thm lemma-2-for-soundness-of-clause.obvious-term-bldr-okp)))
(%use (%instance (%thm forcing-logic.provablep-when-logic.proofp)
(x (clause.obvious-term-bldr (logic.=lhs (logic.~arg (logic.conclusion x)))))))
(%forcingp nil)))
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