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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 "terms")
(%interactive)
(%autoadmit logic.flag-subtermp)
(%autoadmit logic.subtermp)
(%autoadmit logic.subterm-of-somep)
(%autoprove definition-of-logic.subtermp
(%enable default logic.subtermp logic.subterm-of-somep)
(%restrict default logic.flag-subtermp (equal y 'y)))
(%autoprove definition-of-logic.subterm-of-somep
(%enable default logic.subtermp logic.subterm-of-somep)
(%restrict default logic.flag-subtermp (equal y 'y)))
(%autoprove logic.subterm-of-somep-when-not-consp
(%restrict default definition-of-logic.subterm-of-somep (equal y 'x)))
(%autoprove logic.subterm-of-somep-of-cons
(%restrict default definition-of-logic.subterm-of-somep (equal y '(cons b y))))
(%autoprove lemma-for-booleanp-of-logic.subtermp
(%logic.term-induction flag y)
(%restrict default definition-of-logic.subtermp (equal y 'y))
(%disable default
forcing-true-listp-of-logic.function-args
forcing-true-listp-of-logic.lambda-actuals))
(%autoprove booleanp-of-logic.subtermp
(%use (%instance (%thm lemma-for-booleanp-of-logic.subtermp)
(flag 'term))))
(%autoprove booleanp-of-logic.subterm-of-somep
(%use (%instance (%thm lemma-for-booleanp-of-logic.subtermp)
(flag 'list))))
(%autoprove logic.subterm-of-somep-when-memberp-is-logic.subtermp
(%cdr-induction x))
(%autoprove logic.subterm-of-somep-when-memberp-is-logic.subtermp-alt)
(%autoprove logic.subtermp-is-reflexive
(%restrict default definition-of-logic.subtermp (equal x 'x)))
(%autoprove lemma-for-logic.subtermp-is-transitive
(%logic.term-induction flag z)
(%disable default
forcing-true-listp-of-logic.function-args
forcing-true-listp-of-logic.lambda-actuals)
(%auto)
(%restrict default definition-of-logic.subtermp (memberp y '(y z)))
;; strategy reduces from 650M to 200M
(%auto :strategy (cleanup split crewrite elim)))
(%autoprove logic.subtermp-is-transitive
(%use (%instance (%thm lemma-for-logic.subtermp-is-transitive)
(flag 'term))))
(%autoprove logic.subtermp-is-transitive-two)
(%autoprove logic.subterm-of-somep-when-logic.subtermp-and-logic.subterm-of-somep
(%use (%instance (%thm lemma-for-logic.subtermp-is-transitive)
(flag 'list))))
(%autoprove logic.subterm-of-somep-when-logic.subtermp-and-logic.subterm-of-somep-alt)
(%autoprove lemma-for-rank-when-logic.subtermp-weak
(%logic.term-induction flag y)
(%disable default
forcing-true-listp-of-logic.function-args
forcing-true-listp-of-logic.lambda-actuals)
(%auto)
(%restrict default definition-of-logic.subtermp (equal y 'y)))
(%autoprove rank-when-logic.subtermp-weak
(%use (%instance (%thm lemma-for-rank-when-logic.subtermp-weak)
(flag 'term))))
(%autoprove rank-when-logic.subterm-of-somep
(%use (%instance (%thm lemma-for-rank-when-logic.subtermp-weak)
(flag 'list))))
(%autoprove rank-when-logic.subterm-of-somep-weak)
(%autoprove rank-when-logic.subtermp
(%restrict default definition-of-logic.subtermp (equal y 'y))
(%auto)
(%disable default rank-when-logic.subterm-of-somep)
(%use (%instance (%thm rank-when-logic.subterm-of-somep) (x x) (y (logic.function-args y))))
(%auto)
(%use (%instance (%thm rank-when-logic.subterm-of-somep) (x x) (y (logic.lambda-actuals y)))))
(%autoprove logic.subtermp-is-weakly-antisymmetric
(%disable default rank-when-logic.subtermp)
(%use (%instance (%thm rank-when-logic.subtermp))))
(%autoprove logic.subtermp-of-logic.functionp
(%restrict default definition-of-logic.subtermp (equal y '(logic.function fn args))))
(%autoprove logic.subtermp-of-logic.lambda
(%restrict default definition-of-logic.subtermp (equal y '(logic.lambda xs b ts))))
(%autoprove logic.subterm-of-somep-of-list-fix (%cdr-induction x))
(%autoprove logic.subterm-of-somep-of-app (%cdr-induction x))
(%autoprove logic.subterm-of-somep-of-rev (%cdr-induction x))
(%deflist logic.all-subterm-of-somep (x others)
(logic.subterm-of-somep x others))
(%autoprove logic.all-subterm-of-somep-when-not-consp-two (%cdr-induction x))
(%autoprove logic.all-subterm-of-somep-of-cons-two (%cdr-induction x))
(%autoprove logic.all-subterm-of-somep-of-list-fix-two (%cdr-induction x))
(%autoprove logic.all-subterm-of-somep-of-app-two (%cdr-induction x))
(%autoprove logic.all-subterm-of-somep-of-app-two-alt (%cdr-induction x))
(%autoprove logic.all-subterm-of-somep-of-rev-two (%cdr-induction x))
(%autoprove logic.all-subterm-of-somep-is-reflexive (%cdr-induction x))
(%autoprove logic.subterm-of-somep-when-subterm-and-logic.all-subterm-of-somep (%cdr-induction x))
(%autoprove logic.subterm-of-somep-when-subterm-and-logic.all-subterm-of-somep-alt)
(%autoprove logic.all-subterm-of-somep-is-transitive (%cdr-induction x))
(%autoprove logic.all-subterm-of-somep-is-transitive-alt)
(%ensure-exactly-these-rules-are-missing "../../logic/subtermp")
|
