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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 "split")
(include-book "lift-bldr")
(include-book "limlift-bldr")
(%interactive)
(%autoadmit clause.split-bldr)
(%autoprove forcing-logic.appealp-of-clause.split-bldr
(%enable default clause.split clause.split-bldr build.rev-disjunction))
(%autoprove forcing-logic.conclusion-of-clause.split-bldr
(%enable default clause.split clause.split-bldr build.rev-disjunction))
(%autoprove forcing-logic.proofp-of-clause.split-bldr
(%enable default clause.split clause.split-bldr build.rev-disjunction))
(%deflist logic.appeal-list-listp (x)
(logic.appeal-listp x))
(%defprojection :list (logic.strip-conclusions-list x)
:element (logic.strip-conclusions x))
(encapsulate
()
(local (%disable default redefinition-of-clause.clause-list-formulas
[OUTSIDE]REDEFINITION-OF-CLAUSE.CLAUSE-LIST-FORMULAS))
(%defprojection :list (clause.clause-list-list-formulas x)
:element (clause.clause-list-formulas x)))
(%deflist logic.proof-list-listp (x axioms thms atbl)
(logic.proof-listp x axioms thms atbl))
(%autoadmit clause.split-list-bldr)
(%autoprove forcing-logic.appeal-listp-of-clause.split-list-bldr
(%cdr-cdr-induction x proofs)
(%restrict default clause.split-list (equal x 'x))
(%restrict default clause.split-list-bldr (equal x 'x)))
(%autoprove forcing-logic.strip-conclusions-of-clause.split-list-bldr
(%cdr-cdr-induction x proofs)
(%restrict default clause.split-list (equal x 'x))
(%restrict default clause.split-list-bldr (equal x 'x)))
(%autoprove forcing-logic.proof-listp-of-clause.split-list-bldr
(%cdr-cdr-induction x proofs)
(%restrict default clause.split-list (equal x 'x))
(%restrict default clause.split-list-bldr (equal x 'x))
(%disable default
expensive-arithmetic-rules
type-set-like-rules
memberp-when-memberp-of-cdr))
(%autoadmit clause.split-bldr-okp)
(%autoadmit clause.split-bldr-high)
(encapsulate
()
(local (%enable default clause.split-bldr-okp))
(%autoprove booleanp-of-clause.split-bldr-okp)
(%autoprove clause.split-bldr-okp-of-logic.appeal-identity)
(%autoprove lemma-1-for-soundness-of-clause.split-bldr-okp)
(%autoprove lemma-2-for-soundness-of-clause.split-bldr-okp)
(%autoprove forcing-soundness-of-clause.split-bldr-okp
(%enable default
lemma-1-for-soundness-of-clause.split-bldr-okp
lemma-2-for-soundness-of-clause.split-bldr-okp)
(%use (%instance (%thm forcing-logic.provablep-when-logic.proofp)
(x (clause.split-bldr (first (logic.extras x))
(second (logic.extras x))
(third (logic.extras x))
(fourth (logic.extras x))
(logic.provable-list-witness (logic.strip-conclusions (logic.subproofs x))
axioms thms atbl)))))))
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