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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)
(%rwn 1000)
(%urwn 1000)
(local (%max-proof-size 0))
(%autoadmit four-nats-measure)
(%autoprove ordp-of-four-nats-measure
(%enable default four-nats-measure)
(%restrict default ordp
(memberp x '((CONS (CONS '3 (+ '1 A))
(CONS (CONS '2 (+ '1 B))
(CONS (CONS '1 (+ '1 C)) (NFIX D))))
(CONS (CONS '2 (+ '1 B))
(CONS (CONS '1 (+ '1 C)) (NFIX D)))
(CONS (CONS '1 (+ '1 C)) (NFIX D))))))
(%autoprove ord<-of-four-nats-measure
(%enable default four-nats-measure)
(%restrict default ord<
(memberp x '((CONS (CONS '3 (+ '1 A1))
(CONS (CONS '2 (+ '1 B1))
(CONS (CONS '1 (+ '1 C1)) (NFIX D1))))
(CONS (CONS '2 (+ '1 B1))
(CONS (CONS '1 (+ '1 C1)) (NFIX D1)))
(CONS (CONS '1 (+ '1 C1)) (NFIX D1))))))
(defsection rw.cresult
(%autoadmit rw.cresult)
(%autoadmit rw.cresult->data)
(%autoadmit rw.cresult->cache)
(%autoadmit rw.cresult->alimitedp)
(local (%enable default
rw.cresult
rw.cresult->data
rw.cresult->cache
rw.cresult->alimitedp))
(%autoprove rw.cresult-under-iff)
(%autoprove rw.cresult->data-of-rw.cresult)
(%autoprove rw.cresult->cache-of-rw.cresult)
(%autoprove rw.cresult->alimitedp-of-rw.cresult))
(defsection rw.hypresult
(%autoadmit rw.hypresult)
(%autoadmit rw.hypresult->successp)
(%autoadmit rw.hypresult->traces)
(%autoadmit rw.hypresult->cache)
(%autoadmit rw.hypresult->alimitedp)
(local (%enable default
rw.hypresult
rw.hypresult->successp
rw.hypresult->traces
rw.hypresult->cache
rw.hypresult->alimitedp))
(%autoprove rw.hypresult-under-iff)
(%autoprove rw.hypresult->successp-of-rw.hypresult)
(%autoprove rw.hypresult->traces-of-rw.hypresult)
(%autoprove rw.hypresult->cache-of-rw.hypresult)
(%autoprove rw.hypresult->alimitedp-of-rw.hypresult))
(%autoadmit rw.flag-crewrite)
(defsection elimination-of-irrelevant-arguments
(local (%forcingp nil))
(local (%betamode nil))
(%autoprove rw.flag-crewrite-of-term-reduction
(%restrict default rw.flag-crewrite (and (equal flag ''term) (equal x 'x))))
(%autoprove rw.flag-crewrite-of-list-reduction
(%restrict default rw.flag-crewrite (and (equal flag ''list) (equal x 'x))))
(%autoprove rw.flag-crewrite-of-rule-reduction
(%restrict default rw.flag-crewrite (and (equal flag ''rule) (equal x 'x))))
(%autoprove rw.flag-crewrite-of-rules-reduction
(%restrict default rw.flag-crewrite (and (equal flag ''rules) (equal x 'x))))
(%autoprove rw.flag-crewrite-of-hyp-reduction
(%restrict default rw.flag-crewrite (and (equal flag ''hyp) (equal x 'x))))
(%autoprove rw.flag-crewrite-of-hyps-reduction
(%restrict default rw.flag-crewrite (and (equal flag ''hyps) (equal x 'x)))))
(defsection flag-function-wrappers
(%autoadmit rw.crewrite-core)
(%autoadmit rw.crewrite-core-list)
(%autoadmit rw.crewrite-try-rule)
(%autoadmit rw.crewrite-try-rules)
(%autoadmit rw.crewrite-try-match)
(%autoadmit rw.crewrite-try-matches)
(%autoadmit rw.crewrite-relieve-hyp)
(%autoadmit rw.crewrite-relieve-hyps)
(local (%forcingp nil))
(local (%enable default
rw.crewrite-core
rw.crewrite-core-list
rw.crewrite-try-rule
rw.crewrite-try-rules
rw.crewrite-try-match
rw.crewrite-try-matches
rw.crewrite-relieve-hyp
rw.crewrite-relieve-hyps))
(%autoprove rw.flag-crewrite-of-term
(%use (%thm rw.flag-crewrite-of-term-reduction)))
(%autoprove rw.flag-crewrite-of-list
(%use (%thm rw.flag-crewrite-of-list-reduction)))
(%autoprove rw.flag-crewrite-of-rule
(%use (%thm rw.flag-crewrite-of-rule-reduction)))
(%autoprove rw.flag-crewrite-of-rules
(%use (%thm rw.flag-crewrite-of-rules-reduction)))
(%autoprove rw.flag-crewrite-of-match)
(%autoprove rw.flag-crewrite-of-matches)
(%autoprove rw.flag-crewrite-of-hyp
(%use (%thm rw.flag-crewrite-of-hyp-reduction)))
(%autoprove rw.flag-crewrite-of-hyps
(%use (%thm rw.flag-crewrite-of-hyps-reduction))))
(%autoprove equal-with-quoted-list-of-nil)
(defsection proper-definitions-for-flag-wrappers
(local (%forcingp nil))
(local (%rwn 2000))
(local (%disable default
formula-decomposition
expensive-term/formula-inference
expensive-arithmetic-rules
expensive-arithmetic-rules-two
type-set-like-rules
unusual-consp-rules
unusual-memberp-rules
unusual-subsetp-rules
same-length-prefixes-equal-cheap
;; ---
lookup-when-not-consp
rw.trace-list-rhses-when-not-consp
forcing-logic.function-of-logic.function-name-and-logic.function-args-free))
(%autoprove definition-of-rw.crewrite-core
(%use (%instance (%thm rw.flag-crewrite) (flag 'term)))
(%betamode nil)
(%auto)
(%betamode once))
(%autoprove definition-of-rw.crewrite-core-list
(%use (%instance (%thm rw.flag-crewrite) (flag 'list)))
(%betamode nil)
(%auto)
(%betamode once))
(%autoprove definition-of-rw.crewrite-try-rule
(%use (%instance (%thm rw.flag-crewrite) (flag 'rule)))
(%betamode nil)
(%auto)
(%betamode once))
(%autoprove definition-of-rw.crewrite-try-rules
(%use (%instance (%thm rw.flag-crewrite) (flag 'rules)))
(%betamode nil)
(%auto)
(%betamode once))
(%autoprove definition-of-rw.crewrite-try-match
(%use (%instance (%thm rw.flag-crewrite) (flag 'match)))
(%betamode nil)
(%auto)
(%betamode once))
(%autoprove definition-of-rw.crewrite-try-matches
(%use (%instance (%thm rw.flag-crewrite) (flag 'matches)))
(%betamode nil)
(%auto)
(%betamode once))
(%autoprove definition-of-rw.crewrite-relieve-hyp
(%use (%instance (%thm rw.flag-crewrite) (flag 'hyp)))
(%betamode nil)
(%auto)
(%betamode once))
(%autoprove definition-of-rw.crewrite-relieve-hyps
(%use (%instance (%thm rw.flag-crewrite) (flag 'hyps)))
(%betamode nil)
(%auto)
(%betamode once)))
(%autoprove rw.crewrite-core-list-when-not-consp
(%restrict default definition-of-rw.crewrite-core-list (equal x 'x)))
(%autoprove rw.crewrite-core-list-of-cons
(%restrict default definition-of-rw.crewrite-core-list (equal x '(cons a x))))
(%autoprove true-listp-of-rw.cresult->data-of-rw.crewrite-core-list
(%induct (rank x)
((not (consp x))
nil)
((consp x)
(((x (cdr x))
(cache (rw.cresult->cache
(rw.crewrite-core assms (car x) cache iffp blimit rlimit anstack control))))))))
(%autoprove len-of-rw.cresult->data-of-rw.crewrite-core-list$
(%induct (rank x)
((not (consp x))
nil)
((consp x)
(((x (cdr x))
(cache (rw.cresult->cache
(rw.crewrite-core assms (car x) cache iffp blimit rlimit anstack control))))))))
(%autoprove rw.crewrite-try-rules-when-not-consp
(%restrict default definition-of-rw.crewrite-try-rules (equal rule[s] 'rule[s])))
(%autoprove rw.crewrite-try-rules-of-cons
(%restrict default definition-of-rw.crewrite-try-rules (equal rule[s] '(cons rule rules))))
(%autoprove rw.crewrite-try-matches-when-not-consp
(%restrict default definition-of-rw.crewrite-try-matches (equal sigma[s] 'sigma[s])))
(%autoprove rw.crewrite-try-matches-of-cons
(%restrict default definition-of-rw.crewrite-try-matches (equal sigma[s] '(cons sigma sigmas))))
(%autoprove rw.crewrite-relieve-hyps-when-not-consp
(%restrict default definition-of-rw.crewrite-relieve-hyps (equal x 'x)))
(%autoprove rw.crewrite-relieve-hyps-of-cons
(%restrict default definition-of-rw.crewrite-relieve-hyps (equal x '(cons a x))))
(%autoprove booleanp-of-rw.hypresult->successp-of-rw.crewrite-relieve-hyps
(%use (%thm definition-of-rw.crewrite-relieve-hyps)))
(%autoprove zp-of-one-plus)
|
