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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 "clause-basics")
(include-book "rulep")
(%interactive)
(defthm LOGIC.PEQUAL-LIST-OF-CONS-AND-CONS-gross-right
(implies (syntaxp (logic.constantp y))
(equal (logic.pequal-list (cons a x) y)
(if (consp y)
(CONS (LOGIC.PEQUAL a (CAR Y))
(LOGIC.PEQUAL-LIST x (CDR Y)))
nil)))
:hints(("Goal" :expand (logic.pequal-list (cons a x) y))))
(%autoprove LOGIC.PEQUAL-LIST-OF-CONS-AND-CONS-gross-right)
;(local (%disable default LOGIC.FUNCTION-OF-CONS-WITH-DEFECTIVELY-MERGED-CONSTANT))
(%deftheorem rw.crewrite-rule-lemma)
(encapsulate
()
(local (%enable default bust-up-cdr-of-logic.function-args-expensive))
(%defderiv rw.crewrite-rule-lemma-bldr)
(%defderiv rw.disjoined-crewrite-rule-lemma-bldr))
(defsection rw.crewrite-rule-lemma-list-bldr
(%autoadmit rw.crewrite-rule-lemma-list-bldr)
(%autoprove forcing-logic.appeal-listp-of-rw.crewrite-rule-lemma-list-bldr
(%cdr-induction x)
(%restrict default rw.crewrite-rule-lemma-list-bldr (equal x 'x)))
(%autoprove forcing-logic.strip-conclusions-of-rw.crewrite-rule-lemma-list-bldr
(%cdr-induction x)
(%restrict default rw.crewrite-rule-lemma-list-bldr (equal x 'x))
(%enable default logic.negate-term)
(%disable default
formula-decomposition
expensive-term/formula-inference))
(%autoprove forcing-logic.proof-listp-of-rw.crewrite-rule-lemma-list-bldr
(%cdr-induction x)
(%restrict default rw.crewrite-rule-lemma-list-bldr (equal x 'x))))
(defsection rw.disjoined-crewrite-rule-lemma-list-bldr
(%autoadmit rw.disjoined-crewrite-rule-lemma-list-bldr)
(%autoprove forcing-logic.appeal-listp-of-rw.disjoined-crewrite-rule-lemma-list-bldr
(%cdr-induction x)
(%restrict default rw.disjoined-crewrite-rule-lemma-list-bldr (equal x 'x)))
(%autoprove forcing-logic.strip-conclusions-of-rw.disjoined-crewrite-rule-lemma-list-bldr
(%cdr-induction x)
(%restrict default rw.disjoined-crewrite-rule-lemma-list-bldr (equal x 'x))
(%enable default logic.negate-term))
(%autoprove forcing-logic.proof-listp-of-rw.disjoined-crewrite-rule-lemma-list-bldr
(%cdr-induction x)
(%restrict default rw.disjoined-crewrite-rule-lemma-list-bldr (equal x 'x))))
(defsection rw.compile-crewrite-rule-trace-lemma1
(defthmd lemma-for-logic.appealp-of-rw.compile-crewrite-rule-trace-lemma1
;; BOZO unlocalize in ACL2 model
(implies (and (logic.all-negationsp a)
(logic.all-negationsp c)
(force (equal (len a) (len c))) ;; not always true, we force anyway
(force (equal (len b) (len d))) ;; not always true, we force anyway
(force (logic.formula-listp a))
(force (logic.formula-listp b))
(force (logic.formula-listp c))
(force (logic.formula-listp d)))
(equal (equal (logic.disjoin-formulas (app a b))
(logic.disjoin-formulas (app c d)))
(and (equal (list-fix a) (list-fix c))
(equal (list-fix b) (list-fix d))))))
(defthmd lemma2-for-logic.appealp-of-rw.compile-crewrite-rule-trace-lemma1
;; BOZO unlocalize in ACL2 model
(implies (equal (logic.substitute-list (rw.hyp-list-terms (rw.rule->hyps rule)) sigma)
(strip-firsts (logic.strip-function-args (logic.=lhses (logic.strip-conclusions proofs)))))
(equal (len proofs)
(len (rw.rule->hyps rule))))
:hints(("Goal"
:in-theory (disable len-of-strip-firsts len-of-logic.substitute-list)
:use ((:instance len-of-strip-firsts
(x (logic.strip-function-args (logic.=lhses (logic.strip-conclusions proofs)))))
(:instance len-of-logic.substitute-list
(x (rw.hyp-list-terms (rw.rule->hyps rule))))))))
(%autoadmit rw.compile-crewrite-rule-trace-lemma1)
(local (%enable default
rw.compile-crewrite-rule-trace-lemma1
rw.rule-clause
redefinition-of-logic.term-list-formulas))
(%autoprove lemma-for-logic.appealp-of-rw.compile-crewrite-rule-trace-lemma1)
(%autoprove lemma2-for-logic.appealp-of-rw.compile-crewrite-rule-trace-lemma1
(%disable default
len-of-strip-firsts
len-of-logic.substitute-list
[outside]len-of-strip-firsts
[outside]len-of-logic.substitute-list)
(%use (%instance (%thm len-of-strip-firsts)
(x (logic.strip-function-args (logic.=lhses (logic.strip-conclusions proofs))))))
(%use (%instance (%thm len-of-logic.substitute-list)
(x (rw.hyp-list-terms (rw.rule->hyps rule))))))
(local (%enable default
lemma-for-logic.appealp-of-rw.compile-crewrite-rule-trace-lemma1
lemma2-for-logic.appealp-of-rw.compile-crewrite-rule-trace-lemma1))
;; Speed hack
(local (%disable default
consp-when-memberp-of-logic.sigmap
consp-when-memberp-of-logic.sigma-atblp
all-equalp-of-subsetp-when-all-equalp))
(%autoprove logic.appealp-of-rw.compile-crewrite-rule-trace-lemma1)
(%autoprove logic.conclusion-of-rw.compile-crewrite-rule-trace-lemma1)
(%autoprove logic.proofp-of-rw.compile-crewrite-rule-trace-lemma1
(%enable default rw.rule-env-okp)))
(defsection rw.compile-crewrite-rule-trace-lemma2
(defthmd lemma-2-for-logic.appealp-of-rw.compile-crewrite-rule-trace-lemma2
;; BOZO unlocalize. We use lemma-1 from lemma1.
(implies (equal (logic.substitute-list (rw.hyp-list-terms (rw.rule->hyps rule)) sigma)
(strip-firsts (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs))))))
(equal (len proofs)
(len (rw.rule->hyps rule))))
:hints(("Goal"
:in-theory (disable len-of-strip-firsts len-of-logic.substitute-list)
:use ((:instance len-of-strip-firsts
(x (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs))))))
(:instance len-of-logic.substitute-list
(x (rw.hyp-list-terms (rw.rule->hyps rule))))))))
(%autoadmit rw.compile-crewrite-rule-trace-lemma2)
(local (%enable default
rw.compile-crewrite-rule-trace-lemma2
rw.rule-clause
redefinition-of-logic.term-list-formulas))
(%autoprove lemma-2-for-logic.appealp-of-rw.compile-crewrite-rule-trace-lemma2
(%disable default
len-of-strip-firsts
len-of-logic.substitute-list
[outside]len-of-strip-firsts
[outside]len-of-logic.substitute-list)
(%use (%instance (%thm len-of-strip-firsts)
(x (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs)))))))
(%use (%instance (%thm len-of-logic.substitute-list)
(x (rw.hyp-list-terms (rw.rule->hyps rule))))))
(local (%enable default
lemma-for-logic.appealp-of-rw.compile-crewrite-rule-trace-lemma1
lemma-2-for-logic.appealp-of-rw.compile-crewrite-rule-trace-lemma2))
(local (%disable default
consp-when-memberp-of-logic.sigmap
consp-when-memberp-of-logic.sigma-atblp
all-equalp-of-subsetp-when-all-equalp))
(%autoprove forcing-logic.appealp-of-rw.compile-crewrite-rule-trace-lemma2)
(%autoprove forcing-logic.conclusion-of-rw.compile-crewrite-rule-trace-lemma2)
(%autoprove forcing-logic.proofp-of-rw.compile-crewrite-rule-trace-lemma2
(%enable default rw.rule-env-okp)))
(defsection rw.compile-crewrite-rule-trace-lemma1-okp
(%autoadmit rw.compile-crewrite-rule-trace-lemma1-okp)
(%autoprove booleanp-of-rw.compile-crewrite-rule-trace-lemma1-okp
(%enable default rw.compile-crewrite-rule-trace-lemma1-okp))
(%autoprove rw.compile-crewrite-rule-trace-lemma1-okp-of-logic.appeal-identity
(%enable default rw.compile-crewrite-rule-trace-lemma1-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-1-for-soundness-of-rw.compile-crewrite-rule-trace-lemma1-okp
(%enable default rw.compile-crewrite-rule-trace-lemma1-okp))
(%autoprove lemma-2-for-soundness-of-rw.compile-crewrite-rule-trace-lemma1-okp
(%enable default rw.compile-crewrite-rule-trace-lemma1-okp))
(%autoprove forcing-soundness-of-rw.compile-crewrite-rule-trace-lemma1-okp
(%enable default
lemma-1-for-soundness-of-rw.compile-crewrite-rule-trace-lemma1-okp
lemma-2-for-soundness-of-rw.compile-crewrite-rule-trace-lemma1-okp)
(%use (%instance (%thm forcing-logic.provablep-when-logic.proofp)
(x (rw.compile-crewrite-rule-trace-lemma1 (first (logic.extras x))
(second (logic.extras x))
(logic.provable-list-witness
(logic.strip-conclusions (logic.subproofs x))
axioms thms atbl)))))
(%auto :strategy (cleanup split crewrite))
(%enable default rw.compile-crewrite-rule-trace-lemma1-okp)
(%auto :strategy (cleanup split crewrite))))
(defsection rw.compile-crewrite-rule-trace-lemma2-okp
(%autoadmit rw.compile-crewrite-rule-trace-lemma2-okp)
(%autoprove booleanp-of-rw.compile-crewrite-rule-trace-lemma2-okp
(%enable default rw.compile-crewrite-rule-trace-lemma2-okp))
(%autoprove rw.compile-crewrite-rule-trace-lemma2-okp-of-logic.appeal-identity
(%enable default rw.compile-crewrite-rule-trace-lemma2-okp))
(%autoprove lemma-1-for-soundness-of-rw.compile-crewrite-rule-trace-lemma2-okp
(%enable default rw.compile-crewrite-rule-trace-lemma2-okp))
(%autoprove lemma-2-for-soundness-of-rw.compile-crewrite-rule-trace-lemma2-okp
(%enable default rw.compile-crewrite-rule-trace-lemma2-okp))
(%autoprove forcing-soundness-of-rw.compile-crewrite-rule-trace-lemma2-okp
(%enable default
lemma-1-for-soundness-of-rw.compile-crewrite-rule-trace-lemma2-okp
lemma-2-for-soundness-of-rw.compile-crewrite-rule-trace-lemma2-okp)
(%use (%instance (%thm forcing-logic.provablep-when-logic.proofp)
(x (rw.compile-crewrite-rule-trace-lemma2 (first (logic.extras x))
(second (logic.extras x))
(third (logic.extras x))
(logic.provable-list-witness
(logic.strip-conclusions (logic.subproofs x))
axioms thms atbl)))))
(%auto :strategy (cleanup split crewrite))
(%enable default rw.compile-crewrite-rule-trace-lemma2-okp)
(%auto :strategy (cleanup split crewrite))))
|
