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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")
(%interactive)
(local (%enable default lemma-split-up-list-of-quoted-nil))
(%autoadmit clause.normalize-nots-term)
(defmacro %clause.normalize-nots-term-induction (x)
`(%induct (rank ,x)
((not (clause.negative-termp ,x))
nil)
((and (clause.negative-termp ,x)
(not (clause.negative-termp (clause.negative-term-guts ,x))))
nil)
((and (clause.negative-termp ,x)
(clause.negative-termp (clause.negative-term-guts ,x)))
(((,x (clause.negative-term-guts (clause.negative-term-guts ,x))))))))
(%autoprove forcing-logic.termp-of-clause.normalize-nots-term
(%clause.normalize-nots-term-induction x)
(%restrict default clause.normalize-nots-term (equal x 'x)))
(%autoprove forcing-logic.term-atblp-of-clause.normalize-nots-term
(%clause.normalize-nots-term-induction x)
(%restrict default clause.normalize-nots-term (equal x 'x)))
(%autoprove no-double-negatives-after-clause.normalize-nots-term
(%clause.normalize-nots-term-induction x)
(%restrict default clause.normalize-nots-term (equal x 'x)))
(%autoadmit clause.normalize-nots-term-bldr)
(defthmd lemma-1-for-forcing-logic.appealp-of-clause.normalize-nots-term-bldr
;; BOZO need to unlocalize this in the clean-clauses.lisp
;; NOTE -- changing the order of the equality to match term order.
(implies (not (cdr (cdr x)))
(equal (equal 2 (len x))
(and (consp x)
(consp (cdr x))))))
(defthm lemma-2-for-forcing-logic.appealp-of-clause.normalize-nots-term-bldr
;; BOZO need to unlocalize this in the clean-clauses.lisp
(implies (logic.termp a)
(and (logic.appealp (clause.normalize-nots-term-bldr a))
(equal (logic.conclusion (clause.normalize-nots-term-bldr a))
(logic.pequal (logic.function 'iff (list a (clause.normalize-nots-term a)))
''t))))
:rule-classes nil)
(%autoprove lemma-1-for-forcing-logic.appealp-of-clause.normalize-nots-term-bldr)
(%autoprove lemma-2-for-forcing-logic.appealp-of-clause.normalize-nots-term-bldr
(%clause.normalize-nots-term-induction a)
(%enable default lemma-1-for-forcing-logic.appealp-of-clause.normalize-nots-term-bldr)
(%disable default
aggressive-equal-of-logic.pors
aggressive-equal-of-logic.pnots
aggressive-equal-of-logic.pequals)
(%restrict default clause.normalize-nots-term (equal x 'a))
(%restrict default clause.normalize-nots-term-bldr (equal a 'a))
(%enable default theorem-not-of-not-under-iff)
(%disable default
forcing-logic.function-of-logic.function-name-and-logic.function-args-free
equal-of-booleans-rewrite
equal-of-cons-rewrite)
(%auto :strategy (cleanup split urewrite))
(%forcingp t)
(%disable default
EQUAL-OF-LOGIC.FUNCTION-REWRITE-ALT
EQUAL-OF-LOGIC.FUNCTION-REWRITE
equal-of-logic.function-and-logic.function
[outside]equal-of-logic.function-and-logic.function)
(%enable default
equal-of-booleans-rewrite
equal-of-cons-rewrite)
(%auto)
(%enable default
equal-of-logic.function-and-logic.function
[outside]equal-of-logic.function-and-logic.function
EQUAL-OF-LOGIC.FUNCTION-REWRITE-ALT
EQUAL-OF-LOGIC.FUNCTION-REWRITE))
(%autoprove forcing-logic.appealp-of-clause.normalize-nots-term-bldr
(%use (%instance (%thm lemma-2-for-forcing-logic.appealp-of-clause.normalize-nots-term-bldr))))
(%autoprove forcing-logic.conclusion-of-clause.normalize-nots-term-bldr
(%use (%instance (%thm lemma-2-for-forcing-logic.appealp-of-clause.normalize-nots-term-bldr))))
(%autoprove forcing-logic.proofp-of-clause.normalize-nots-term-bldr
(%clause.normalize-nots-term-induction a)
(%restrict default clause.normalize-nots-term (equal x 'a))
(%restrict default clause.normalize-nots-term-bldr (equal a 'a))
(%enable default theorem-not-of-not-under-iff))
(%defprojection :list (clause.normalize-nots-term-list x)
:element (clause.normalize-nots-term x))
(%autoprove forcing-logic.term-listp-of-clause.normalize-nots-term-list
(%cdr-induction x))
(%autoprove forcing-logic.term-list-atblp-of-clause.normalize-nots-term-list
(%cdr-induction x))
(%autoprove clause.double-negative-free-listp-of-clause.normalize-nots-term-list
(%cdr-induction x))
(%defprojection :list (clause.normalize-nots-term-list-bldr x)
:element (clause.normalize-nots-term-bldr x))
(%autoprove forcing-logic.appeal-listp-of-clause.normalize-nots-term-list-bldr
(%cdr-induction x))
(%autoprove forcing-logic.strip-conclusions-of-clause.normalize-nots-term-list-bldr
(%cdr-induction x)
;; bleh why are we having rlimit loops here?
(%auto :strategy (cleanup split urewrite elim)))
(%autoprove forcing-logic.proof-listp-of-clause.normalize-nots-term-list-bldr
(%cdr-induction x)
;; bleh why are we having rlimit loops here?
(%auto :strategy (cleanup split urewrite elim)))
(%defprojection :list (clause.normalize-nots-clauses x)
:element (clause.normalize-nots-term-list x))
(%autoprove forcing-logic.term-list-listp-of-clause.normalize-nots-clauses
(%cdr-induction x))
(%autoprove forcing-logic.term-list-list-atblp-of-clause.normalize-nots-clauses
(%cdr-induction x))
(%autoprove cons-listp-of-clause.normalize-nots-clauses
(%cdr-induction x))
(%autoadmit clause.normalize-nots-clauses-bldr)
(%autoprove forcing-logic.appeal-listp-of-clause.normalize-nots-clauses-bldr
(%cdr-cdr-induction x proofs)
(%restrict default clause.normalize-nots-clauses-bldr (equal x 'x)))
(%autoprove forcing-logic.strip-conclusions-of-clause.normalize-nots-clauses-bldr
(%cdr-cdr-induction x proofs)
(%restrict default clause.normalize-nots-clauses-bldr (equal x 'x)))
(%autoprove forcing-logic.proof-listp-of-clause.normalize-nots-clauses-bldr
(%cdr-cdr-induction x proofs)
(%restrict default clause.normalize-nots-clauses-bldr (equal x 'x)))
|
