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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 "pequal-list")
(%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))
(%autoadmit clause.clause-formula)
(%autoprove redefinition-of-clause.clause-formula
(%cdr-induction x)
(%restrict default clause.clause-formula (equal x 'x))
(%forcingp nil))
(%autoadmit clause.clause-list-formulas)
(%autoprove redefinition-of-clause.clause-list-formulas
(%cdr-induction x)
(%restrict default clause.clause-list-formulas (equal x 'x)))
(%autoadmit clause.negative-termp)
(%autoprove booleanp-of-clause.negative-termp
(%enable default clause.negative-termp)
(%forcingp nil))
(%autoprove clause.negative-termp-of-logic.function-of-not
(%enable default clause.negative-termp)
(%forcingp nil))
(%autoprove logic.functionp-when-clause.negative-termp
(%enable default clause.negative-termp))
(%enable expensive-term/formula-inference
logic.functionp-when-clause.negative-termp)
(%autoadmit clause.negative-term-guts)
(%autoprove forcing-logic.termp-of-clause.negative-term-guts
(%enable default clause.negative-termp clause.negative-term-guts))
(%autoprove forcing-logic.term-atblp-of-clause.negative-term-guts
(%enable default clause.negative-termp clause.negative-term-guts))
(%autoprove clause.negative-term-guts-of-logic.function-of-not
(%enable default clause.negative-term-guts))
(%autoprove rank-of-clause.negative-term-guts-when-clause.negative-termp
(%enable default
clause.negative-term-guts
clause.negative-termp
logic.function-args))
(%autoprove rank-of-clause.negative-term-guts-of-clause.negative-term-guts
(%disable default rank-of-clause.negative-term-guts-when-clause.negative-termp)
(%use (%instance (%thm rank-of-clause.negative-term-guts-when-clause.negative-termp)
(x (clause.negative-term-guts x))))
(%use (%instance (%thm rank-of-clause.negative-term-guts-when-clause.negative-termp))))
(%autoadmit clause.term-guts)
(%autoprove forcing-logic.termp-of-clause.term-guts
(%enable default clause.term-guts))
(%autoprove forcing-logic.term-atblp-of-clause.term-guts
(%enable default clause.term-guts))
(%defprojection :list (clause.term-list-guts x)
:element (clause.term-guts x)
:nil-preservingp t)
(%autoprove forcing-logic.term-listp-of-clause.term-list-guts
(%cdr-induction x))
(%autoprove forcing-logic.term-list-atblp-of-clause.term-list-guts
(%cdr-induction x))
(%autoadmit definition-of-not)
(%noexec definition-of-not)
(%defderiv clause.substitute-iff-into-literal-bldr)
(encapsulate
()
;; previously 1.7 BN
(local (%max-proof-size 1000000000))
(%defderiv clause.disjoined-substitute-iff-into-literal-bldr))
(%deftheorem clause.theorem-standardize-equal-x-nil)
(%deftheorem clause.theorem-standardize-equal-nil-x)
(%deftheorem clause.theorem-standardize-iff-x-nil)
(%deftheorem clause.theorem-standardize-iff-nil-x)
(defsection clause.standardize-negative-term-bldr
(%autoadmit clause.standardize-negative-term-bldr)
(local (%enable default
clause.standardize-negative-term-bldr
clause.negative-termp
clause.negative-term-guts
definition-of-not
clause.theorem-standardize-equal-nil-x
clause.theorem-standardize-equal-x-nil
clause.theorem-standardize-iff-nil-x
clause.theorem-standardize-iff-x-nil))
(%autoprove forcing-logic.appealp-of-clause.standardize-negative-term-bldr)
(%autoprove forcing-logic.conclusion-of-clause.standardize-negative-term-bldr)
(%autoprove forcing-logic.proofp-of-clause.standardize-negative-term-bldr))
(defsection clause.standardize-negative-term-bldr-okp
(%autoadmit clause.standardize-negative-term-bldr-okp)
(local (%enable default clause.standardize-negative-term-bldr-okp))
(%autoprove booleanp-of-clause.standardize-negative-term-bldr-okp)
(%autoprove clause.standardize-negative-term-bldr-okp-of-logic.appeal-identity)
(%autoprove lemma-1-for-soundness-of-clause.standardize-negative-term-bldr-okp)
(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-2-for-soundness-of-clause.standardize-negative-term-bldr-okp)
(%autoprove forcing-soundness-of-clause.standardize-negative-term-bldr-okp
(%enable default
lemma-1-for-soundness-of-clause.standardize-negative-term-bldr-okp
lemma-2-for-soundness-of-clause.standardize-negative-term-bldr-okp)
(%use (%instance (%thm forcing-logic.provablep-when-logic.proofp)
(x (clause.standardize-negative-term-bldr (logic.=lhs (logic.conclusion x))))))))
(defsection clause.standardize-double-negative-term-bldr
(%autoadmit clause.standardize-double-negative-term-bldr)
(local (%enable default clause.standardize-double-negative-term-bldr))
(%autoprove forcing-logic.appealp-of-clause.standardize-double-negative-term-bldr)
(%autoprove forcing-logic.conclusion-of-clause.standardize-double-negative-term-bldr)
(%autoprove forcing-logic.proofp-of-clause.standardize-double-negative-term-bldr))
(defsection clause.standardize-double-negative-term-bldr-okp
(%autoadmit clause.standardize-double-negative-term-bldr-okp)
(local (%enable default clause.standardize-double-negative-term-bldr-okp))
(%autoprove booleanp-of-clause.standardize-double-negative-term-bldr-okp)
(%autoprove clause.standardize-double-negative-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.standardize-double-negative-term-bldr-okp)
(%autoprove lemma-2-for-soundness-of-clause.standardize-double-negative-term-bldr-okp)
(%autoprove forcing-soundness-of-clause.standardize-double-negative-term-bldr-okp
(%enable default
lemma-1-for-soundness-of-clause.standardize-double-negative-term-bldr-okp
lemma-2-for-soundness-of-clause.standardize-double-negative-term-bldr-okp)
(%use (%instance (%thm forcing-logic.provablep-when-logic.proofp)
(x (clause.standardize-double-negative-term-bldr (logic.=lhs (logic.conclusion x))))))))
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