; 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 "skeletonp")
(include-book "split-all") ;; BOZO yuck for cons-listp-of-list-list-fix ??
(%interactive)

(%autoprove true-list-listp-of-remove-supersets1
            (%autoinduct remove-supersets1 x acc)
            (%restrict default remove-supersets1 (equal todo 'x)))

(%autoprove true-list-listp-of-remove-supersets
            (%enable default remove-supersets))

(%autoprove true-list-listp-of-remove-duplicates-list
            (%cdr-induction x))

(%autoprove true-list-listp-of-third-of-clause.clean-clauses
            (%enable default clause.clean-clauses))

(%autoprove true-list-listp-of-third-of-clause.fast-clean-clauses
            (%enable default clause.fast-clean-clauses)
            (%disable default
                      clause.fast-clean-clauses-removal
                      clause.fast-clean-part1-removal))

(%autoprove true-list-listp-of-revappend
            (%autoinduct revappend x acc)
            (%restrict default revappend (equal x 'x))
            (%disable default forcing-revappend-removal))

(%autoprove true-list-listp-of-clause.aux-split
            (%autoinduct clause.aux-split)
            (%restrict default clause.aux-split (equal todo 'todo)))

(%autoprove true-list-listp-of-clause.aux-limsplit
            (%autoinduct clause.aux-limsplit todo done splitlimit)
            (%restrict default clause.aux-limsplit (equal todo 'todo)))

(%autoprove true-list-listp-of-clause.simple-limsplit
            (%enable default clause.simple-limsplit))

(%autoprove true-list-listp-of-clause.simple-split
            (%enable default clause.simple-split))

(%autoprove true-list-listp-of-cdr-of-clause.split
            (%forcingp nil)
            (%enable default clause.split))

(%autoprove logic.formula-listp-of-remove-duplicates-free)

(%autoprove logic.formula-list-atblp-of-remove-duplicates-free)

(%autoprove subsetp-of-remove-duplicates-one-indirect)

;; this is now included as part of split-all to avoid overwriting files.
;; (%autoprove cons-listp-of-list-list-fix
;;             (%cdr-induction x))

(%autoprove true-list-listp-of-list-list-fix
            (%cdr-induction x))

(%autoprove logic.term-list-listp-of-list-list-fix
            (%cdr-induction x))

(%autoprove list-list-fix-when-true-list-listp
            (%cdr-induction x))

(%autoprove logic.term-list-list-atblp-of-list-list-fix
            (%cdr-induction x))


(%autoadmit rw.flag-waterstepp)

(%autoadmit rw.waterstepp)

(%autoadmit rw.waterstep-listp)

(%autoprove definition-of-rw.waterstepp
            (%restrict default rw.flag-waterstepp (equal x 'x))
            (%enable default rw.waterstepp rw.waterstep-listp))

(%autoprove definition-of-rw.waterstep-listp
            (%restrict default rw.flag-waterstepp (equal x 'x))
            (%enable default rw.waterstepp rw.waterstep-listp))

(%autoprove rw.waterstep-listp-when-not-consp
            (%restrict default definition-of-rw.waterstep-listp (equal x 'x)))

(%autoprove rw.waterstep-listp-of-cons
            (%restrict default definition-of-rw.waterstep-listp (equal x '(cons a x))))

(%autoadmit rw.raw-waterstep-induction)

(%autoprove lemma-for-booleanp-of-rw.waterstepp
            (%autoinduct rw.raw-waterstep-induction flag x)
            (%restrict default definition-of-rw.waterstepp (equal x 'x)))

(%autoprove booleanp-of-rw.waterstepp
            (%use (%instance (%thm lemma-for-booleanp-of-rw.waterstepp)
                             (flag 'clause))))

(%autoprove booleanp-of-rw.waterstep-listp
            (%use (%instance (%thm lemma-for-booleanp-of-rw.waterstepp)
                             (flag 'list))))

(%deflist rw.waterstep-listp (x)
          (rw.waterstepp x))


(%autoadmit rw.waterstep)
(%autoadmit rw.waterstep->method)
(%autoadmit rw.waterstep->clause)
(%autoadmit rw.waterstep->extras)
(%autoadmit rw.waterstep->substeps)

(encapsulate
 ()
 (local (%enable default
                 rw.waterstep
                 rw.waterstep->method
                 rw.waterstep->clause
                 rw.waterstep->extras
                 rw.waterstep->substeps))
 (%autoprove rw.waterstep->method-of-rw.waterstep)
 (%autoprove rw.waterstep->clause-of-rw.waterstep)
 (%autoprove rw.waterstep->extras-of-rw.waterstep)
 (%autoprove rw.waterstep->substeps-of-rw.waterstep)
 (%autoprove rank-of-rw.waterstep->substeps)

 (%autoprove rw.waterstepp-of-rw.waterstep
             (%restrict default definition-of-rw.waterstepp
                        (and (logic.functionp x)
                             (equal (logic.function-name x) 'cons))))

 (%autoprove symbolp-of-rw.waterstep->method
             (%restrict default definition-of-rw.waterstepp (equal x 'x)))

 (%autoprove logic.term-listp-of-rw.waterstep->clause
             (%restrict default definition-of-rw.waterstepp (equal x 'x)))

 (%autoprove consp-of-rw.waterstep->clause
             (%restrict default definition-of-rw.waterstepp (equal x 'x)))

 (%autoprove true-listp-of-rw.waterstep->clause
             (%restrict default definition-of-rw.waterstepp (equal x 'x)))

 (%autoprove rw.waterstep-listp-of-rw.waterstep->substeps
             (%restrict default definition-of-rw.waterstepp (equal x 'x))))



(%defprojection :list (rw.waterstep-list->clauses x)
                :element (rw.waterstep->clause x)
                :nil-preservingp t)

(%autoprove cons-listp-of-rw.waterstep-list->clauses
            (%cdr-induction x))

(%autoprove true-list-listp-of-rw.waterstep-list->clauses
            (%cdr-induction x))

(%autoprove logic.term-list-listp-of-rw.waterstep-list->clauses
            (%cdr-induction x))


(%autoadmit rw.waterstep-induction)

(%autoadmit rw.flag-waterstep-atblp)
(%autoadmit rw.waterstep-atblp)
(%autoadmit rw.waterstep-list-atblp)

(%autoprove definition-of-rw.waterstep-atblp
            (%restrict default rw.flag-waterstep-atblp (equal x 'x))
            (%enable default rw.waterstep-atblp rw.waterstep-list-atblp))

(%autoprove definition-of-rw.waterstep-list-atblp
            (%restrict default rw.flag-waterstep-atblp (equal x 'x))
            (%enable default rw.waterstep-atblp rw.waterstep-list-atblp))

(%autoprove rw.flag-waterstep-atblp-of-clause
            (%enable default rw.waterstep-atblp))

(%autoprove rw.flag-waterstep-list-atblp-of-clause
            (%enable default rw.waterstep-list-atblp))

(%autoprove rw.waterstep-list-atblp-when-not-consp
            (%restrict default definition-of-rw.waterstep-list-atblp (equal x 'x)))

(%autoprove rw.waterstep-list-atblp-of-cons
            (%restrict default definition-of-rw.waterstep-list-atblp (equal x '(cons a x))))

(%autoprove rw.waterstep-atblp-of-nil
            (%restrict default definition-of-rw.waterstep-atblp (equal x ''nil)))

(%autoprove lemma-for-booleanp-of-rw.waterstep-atblp
            (%autoinduct rw.waterstep-induction flag x)
            (%restrict default definition-of-rw.waterstep-atblp (equal x 'x)))

(%autoprove booleanp-of-rw.waterstep-atblp
            (%use (%instance (%thm lemma-for-booleanp-of-rw.waterstep-atblp)
                             (flag 'clause))))

(%autoprove booleanp-of-rw.waterstep-list-atblp
            (%use (%instance (%thm lemma-for-booleanp-of-rw.waterstep-atblp)
                             (flag 'list))))


(%deflist rw.waterstep-list-atblp (x atbl)
          (rw.waterstep-atblp x atbl))

(%autoprove logic.term-list-atblp-of-rw.waterstep->clause
            (%restrict default definition-of-rw.waterstep-atblp (equal x 'x)))

(%autoprove rw.waterstep-list-atblp-of-rw.waterstep->substeps
            (%restrict default definition-of-rw.waterstep-atblp (equal x 'x)))

(%autoprove rw.waterstep-atblp-of-rw.waterstep
            (%restrict default definition-of-rw.waterstep-atblp
                       (equal x '(rw.waterstep method clause extras substeps))))


(%autoadmit rw.stop-waterstep-okp)
(%autoprove booleanp-of-rw.stop-waterstep-okp
            (%enable default rw.stop-waterstep-okp))

(%autoadmit rw.urewrite-waterstep-okp)
(%autoprove booleanp-of-rw.urewrite-waterstep-okp
            (%enable default rw.urewrite-waterstep-okp))

(%autoadmit rw.crewrite-waterstep-okp)
(%autoprove booleanp-of-rw.crewrite-waterstep-okp
            (%enable default rw.crewrite-waterstep-okp))

(%autoadmit rw.split-waterstep-okp)
(%autoprove booleanp-of-rw.split-waterstep-okp
            (%enable default rw.split-waterstep-okp))


(%autoadmit rw.flag-waterstep-okp)
(%autoadmit rw.waterstep-okp)
(%autoadmit rw.waterstep-list-okp)
(%autoprove definition-of-rw.waterstep-okp
            (%restrict default rw.flag-waterstep-okp (equal x 'x))
            (%enable default rw.waterstep-okp rw.waterstep-list-okp))
(%autoprove definition-of-rw.waterstep-list-okp
            (%restrict default rw.flag-waterstep-okp (equal x 'x))
            (%enable default rw.waterstep-okp rw.waterstep-list-okp))

(%autoprove rw.waterstep-list-okp-when-not-consp
            (%restrict default definition-of-rw.waterstep-list-okp (equal x 'x)))
(%autoprove rw.waterstep-list-okp-of-cons
            (%restrict default definition-of-rw.waterstep-list-okp (equal x '(cons a x))))

(%autoprove rw.waterstep-okp-of-nil
            (%restrict default definition-of-rw.waterstep-okp (equal x ''nil)))

(%autoprove lemma-for-booleanp-of-rw.waterstep-okp
            (%autoinduct rw.waterstep-induction flag x)
            (%restrict default definition-of-rw.waterstep-okp (equal x 'x)))

(%autoprove booleanp-of-rw.waterstep-okp
            (%use (%instance (%thm lemma-for-booleanp-of-rw.waterstep-okp)
                             (flag 'clause))))

(%autoprove booleanp-of-rw.waterstep-list-okp
            (%use (%instance (%thm lemma-for-booleanp-of-rw.waterstep-okp)
                             (flag 'list))))

(%deflist rw.waterstep-list-okp (x world)
          (rw.waterstep-okp x world))



(%autoadmit rw.flag-waterfall-subgoals)
(%autoadmit rw.waterfall-subgoals)
(%autoadmit rw.waterfall-list-subgoals)

(%autoprove definition-of-rw.waterfall-subgoals
            (%enable default rw.waterfall-subgoals rw.waterfall-list-subgoals)
            (%restrict default rw.flag-waterfall-subgoals (equal x 'x)))

(%autoprove definition-of-rw.waterfall-list-subgoals
            (%enable default rw.waterfall-subgoals rw.waterfall-list-subgoals)
            (%restrict default rw.flag-waterfall-subgoals (equal x 'x)))

(%autoprove rw.flag-waterfall-subgoals-of-clause
            (%enable default rw.waterfall-subgoals))

(%autoprove rw.flag-waterfall-list-subgoals-of-clause
            (%enable default rw.waterfall-list-subgoals))

(%autoprove rw.waterfall-list-subgoals-when-not-consp
            (%restrict default definition-of-rw.waterfall-list-subgoals (equal x 'x)))

(%autoprove rw.waterfall-list-subgoals-of-cons
            (%restrict default definition-of-rw.waterfall-list-subgoals (equal x '(cons a x))))

(%autoprove lemma-for-logic.term-list-listp-of-rw.waterfall-subgoals
            (%autoinduct rw.flag-waterfall-subgoals flag x)
            (%restrict default definition-of-rw.waterfall-subgoals (equal x 'x)))

(%autoprove logic.term-list-listp-of-rw.waterfall-subgoals
            (%use (%instance (%thm lemma-for-logic.term-list-listp-of-rw.waterfall-subgoals)
                             (flag 'clause))))

(%autoprove logic.term-list-listp-of-rw.waterfall-list-subgoals
            (%use (%instance (%thm lemma-for-logic.term-list-listp-of-rw.waterfall-subgoals)
                             (flag 'list))))

(%autoprove lemma-for-cons-listp-of-rw.waterfall-subgoals
            (%autoinduct rw.flag-waterfall-subgoals flag x)
            (%restrict default definition-of-rw.waterfall-subgoals (equal x 'x)))

(%autoprove cons-listp-of-rw.waterfall-subgoals
            (%use (%instance (%thm lemma-for-cons-listp-of-rw.waterfall-subgoals)
                             (flag 'clause))))

(%autoprove cons-listp-of-rw.waterfall-list-subgoals
            (%use (%instance (%thm lemma-for-cons-listp-of-rw.waterfall-subgoals)
                             (flag 'list))))

(%autoprove lemma-for-true-list-listp-of-rw.waterfall-subgoals
            (%autoinduct rw.flag-waterfall-subgoals flag x)
            (%restrict default definition-of-rw.waterfall-subgoals (equal x 'x)))

(%autoprove true-list-listp-of-rw.waterfall-subgoals
            (%use (%instance (%thm lemma-for-true-list-listp-of-rw.waterfall-subgoals)
                             (flag 'clause))))

(%autoprove true-list-listp-rw.waterfall-list-subgoals
            (%use (%instance (%thm lemma-for-true-list-listp-of-rw.waterfall-subgoals)
                             (flag 'list))))

(%autoprove lemma-for-true-listp-of-rw.waterfall-subgoals
            (%autoinduct rw.flag-waterfall-subgoals flag x)
            (%restrict default definition-of-rw.waterfall-subgoals (equal x 'x)))

(%autoprove true-listp-of-rw.waterfall-subgoals
            (%use (%instance (%thm lemma-for-true-listp-of-rw.waterfall-subgoals)
                             (flag 'clause))))

(%autoprove true-listp-rw.waterfall-list-subgoals
            (%use (%instance (%thm lemma-for-true-listp-of-rw.waterfall-subgoals)
                             (flag 'list))))