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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 "hacks")
(%interactive)
;(local (%disable default LOGIC.FUNCTION-OF-CONS-WITH-DEFECTIVELY-MERGED-CONSTANT))
(defsection build.modus-ponens-list
(encapsulate
()
(%autoadmit build.modus-ponens-list)
(local (%restrict default build.modus-ponens-list (equal as 'as)))
(%autoprove forcing-build.modus-ponens-list-under-iff
(%autoinduct build.modus-ponens-list))
(%autoprove forcing-logic.appealp-of-build.modus-ponens-list
(%autoinduct build.modus-ponens-list))
(%autoprove forcing-logic.conclusion-of-build.modus-ponens-list
(%autoinduct build.modus-ponens-list))
(%autoprove forcing-logic.proofp-of-build.modus-ponens-list
(%autoinduct build.modus-ponens-list)))
(%autoadmit build.modus-ponens-list-okp)
(local (%enable default build.modus-ponens-list-okp))
(%autoprove booleanp-of-build.modus-ponens-list-okp)
(%autoprove build.modus-ponens-list-okp-of-logic.appeal-identity)
(local (%enable default backtracking-logic.formula-atblp-rules))
(local (%disable default
forcing-logic.formula-atblp-rules
forcing-lookup-of-logic.function-name-free
forcing-logic.term-list-atblp-of-logic.function-args))
(%autoprove lemma-1-for-soundness-of-build.modus-ponens-list-okp)
(%autoprove lemma-2-for-soundness-of-build.modus-ponens-list-okp)
(%autoprove forcing-soundness-of-build.modus-ponens-list-okp
(%enable default
lemma-1-for-soundness-of-build.modus-ponens-list-okp
lemma-2-for-soundness-of-build.modus-ponens-list-okp)
(%use (%instance (%thm forcing-logic.provablep-when-logic.proofp)
(x (build.modus-ponens-list (logic.conclusion x)
(logic.provable-list-witness
(logic.strip-conclusions (cdr (logic.subproofs x)))
axioms thms atbl)
(logic.provable-witness
(logic.conclusion (car (logic.subproofs x)))
axioms thms atbl)))))
(%auto :strategy (cleanup split crewrite))))
(defsection build.disjoined-modus-ponens-list
(%autoadmit build.disjoined-modus-ponens-list)
(%autoprove forcing-build.disjoined-modus-ponens-list-under-iff
(%restrict default build.disjoined-modus-ponens-list (equal as 'as))
(%autoinduct build.disjoined-modus-ponens-list))
(%autoprove lemma-for-forcing-logic.appealp-of-build.disjoined-modus-ponens-list
(%autoinduct build.disjoined-modus-ponens-list)
(%restrict default build.disjoined-modus-ponens-list (equal as 'as))
;; This disable prevents an rlimit loop. It wasn't clear to me how to syntactically
;; limit the rule appropriately.
(%disable default forcing-logic.vrhs-of-logic.disjoin-formulas-free))
(%autoprove forcing-logic.appealp-of-build.disjoined-modus-ponens-list
(%use (%instance (%thm lemma-for-forcing-logic.appealp-of-build.disjoined-modus-ponens-list))))
(%autoprove forcing-logic.conclusion-of-build.disjoined-modus-ponens-list
(%use (%instance (%thm lemma-for-forcing-logic.appealp-of-build.disjoined-modus-ponens-list))))
(%autoprove forcing-logic.proofp-of-build.disjoined-modus-ponens-list
(%restrict default build.disjoined-modus-ponens-list (equal as 'as))
(%autoinduct build.disjoined-modus-ponens-list))
(%autoadmit build.disjoined-modus-ponens-list-okp)
(local (%enable default build.disjoined-modus-ponens-list-okp))
(%autoprove booleanp-of-build.disjoined-modus-ponens-list-okp)
(%autoprove build.disjoined-modus-ponens-list-okp-of-logic.appeal-identity)
(local (%enable default backtracking-logic.formula-atblp-rules))
(local (%disable default
forcing-logic.formula-atblp-rules
forcing-lookup-of-logic.function-name-free
forcing-logic.term-list-atblp-of-logic.function-args))
(%autoprove lemma-1-for-soundness-of-build.disjoined-modus-ponens-list-okp)
(%autoprove lemma-2-for-soundness-of-build.disjoined-modus-ponens-list-okp)
(%autoprove forcing-soundness-of-build.disjoined-modus-ponens-list-okp
(%enable default
lemma-1-for-soundness-of-build.disjoined-modus-ponens-list-okp
lemma-2-for-soundness-of-build.disjoined-modus-ponens-list-okp)
(%use (%instance (%thm forcing-logic.provablep-when-logic.proofp)
(x (build.disjoined-modus-ponens-list (logic.vrhs (logic.conclusion x))
(logic.provable-list-witness
(logic.strip-conclusions (cdr (logic.subproofs x)))
axioms thms atbl)
(logic.provable-witness
(logic.conclusion (car (logic.subproofs x)))
axioms thms atbl)))))
(%auto :strategy (cleanup split crewrite))))
(defsection build.multi-expansion
;; No okp --- we use generic-subset instead
(%autoadmit build.multi-expansion)
(local (%restrict default build.multi-expansion (equal as 'as)))
(%autoprove build.multi-expansion-under-iff)
(local (%disable default
car-when-memberp-and-not-memberp-of-cdr-cheap
car-when-memberp-of-singleton-list-cheap))
(%autoprove forcing-logic.appealp-of-build.multi-expansion
(%cdr-induction as)
(%auto)
(%enable default
car-when-memberp-and-not-memberp-of-cdr-cheap
car-when-memberp-of-singleton-list-cheap))
(%autoprove forcing-logic.conclusion-of-build.multi-expansion
(%cdr-induction as)
(%auto)
(%enable default
car-when-memberp-and-not-memberp-of-cdr-cheap
car-when-memberp-of-singleton-list-cheap))
(%autoprove forcing-logic.proofp-of-build.multi-expansion
(%cdr-induction as)
(%auto)
(%enable default
car-when-memberp-and-not-memberp-of-cdr-cheap
car-when-memberp-of-singleton-list-cheap)))
(defsection build.multi-or-expansion-step
;; No okp --- we use generic subset instead
(%autoadmit build.multi-or-expansion-step)
(%autoprove build.multi-or-expansion-step-under-iff
(%restrict default build.multi-or-expansion-step (equal as 'as)))
(local (%disable default
car-when-memberp-of-singleton-list-cheap
car-when-memberp-and-not-memberp-of-cdr-cheap))
(%autoprove lemma-for-forcing-logic.appealp-of-build.multi-or-expansion-step
(%cdr-induction as)
(%restrict default build.multi-or-expansion-step (equal as 'as))
(%auto)
(%enable default
car-when-memberp-of-singleton-list-cheap
car-when-memberp-and-not-memberp-of-cdr-cheap))
(%autoprove forcing-logic.appealp-of-build.multi-or-expansion-step
(%use (%instance (%thm lemma-for-forcing-logic.appealp-of-build.multi-or-expansion-step))))
(%autoprove forcing-logic.conclusion-of-build.multi-or-expansion-step
(%use (%instance (%thm lemma-for-forcing-logic.appealp-of-build.multi-or-expansion-step))))
(%autoprove forcing-logic.proofp-of-build.multi-or-expansion-step
(%cdr-induction as)
(%restrict default build.multi-or-expansion-step (equal as 'as))
(%auto)
(%enable default
car-when-memberp-of-singleton-list-cheap
car-when-memberp-and-not-memberp-of-cdr-cheap)))
(defsection build.multi-or-expansion
;; No okp --- we use generic subset instead
(%autoadmit build.multi-or-expansion)
(local (%restrict default build.multi-or-expansion (equal as 'as)))
(%autoprove build.multi-or-expansion-under-iff)
;; loops with new rewriting changes
(local (%disable default car-when-memberp-and-not-memberp-of-cdr-cheap))
(%autoprove forcing-logic.appealp-of-build.multi-or-expansion
(%cdr-induction as))
(%autoprove forcing-logic.conclusion-of-build.multi-or-expansion
(%cdr-induction as))
(%autoprove forcing-logic.proofp-of-build.multi-or-expansion
(%cdr-induction as)))
(%defderiv build.generic-subset-step-lemma-1 :omit-okp t)
(defsection build.generic-subset-step
;; No okp --- we use generic subset instead
(%autoadmit build.generic-subset-step)
(local (%enable default build.generic-subset-step))
(%autoprove build.generic-subset-step-under-iff)
(%autoprove forcing-logic.appealp-of-build.generic-subset-step)
(%autoprove forcing-logic.conclusion-of-build.generic-subset-step)
(%autoprove forcing-logic.proofp-of-build.generic-subset-step))
(defsection build.generic-subset
(%autoadmit build.generic-subset)
(%autoprove build.generic-subset-under-iff
(%restrict default build.generic-subset (equal as 'as)))
(%autoprove lemma-for-forcing-logic.appealp-of-build.generic-subset
(%autoinduct build.generic-subset)
(%auto :strategy (cleanup split urewrite crewrite))
(%restrict default build.generic-subset (equal as 'as)))
(%autoprove forcing-logic.appealp-of-build.generic-subset
(%use (%instance (%thm lemma-for-forcing-logic.appealp-of-build.generic-subset))))
(%autoprove forcing-logic.conclusion-of-build.generic-subset
(%use (%instance (%thm lemma-for-forcing-logic.appealp-of-build.generic-subset))))
(%autoprove forcing-logic.proofp-of-build.generic-subset
(%autoinduct build.generic-subset)
(%auto :strategy (cleanup split urewrite crewrite))
(%restrict default build.generic-subset (equal as 'as)))
(%autoadmit build.generic-subset-okp)
(local (%enable default build.generic-subset-okp))
(%autoprove booleanp-of-build.generic-subset-okp)
(%autoprove build.generic-subset-okp-of-logic.appeal-identity)
(%autoprove forcing-soundness-of-build.generic-subset-okp
(%use (%instance (%thm forcing-logic.provablep-when-logic.proofp)
(x (build.generic-subset (first (logic.extras x))
(second (logic.extras x))
(logic.provable-witness (logic.conclusion (car (logic.subproofs x)))
axioms thms atbl)))))))
(defsection build.multi-assoc-expansion
(%autoadmit build.multi-assoc-expansion)
(%autoprove build.multi-assoc-expansion-under-iff
(%restrict default build.multi-assoc-expansion (equal as 'as)))
(%autoprove lemma-for-forcing-logic.appealp-of-build.multi-assoc-expansion
(%autoinduct build.multi-assoc-expansion)
(%restrict default build.multi-assoc-expansion (equal as 'as))
(%forcingp nil))
(%autoprove forcing-logic.appealp-of-build.multi-assoc-expansion
(%use (%instance (%thm lemma-for-forcing-logic.appealp-of-build.multi-assoc-expansion))))
(%autoprove forcing-logic.conclusion-of-build.multi-assoc-expansion
(%use (%instance (%thm lemma-for-forcing-logic.appealp-of-build.multi-assoc-expansion))))
(%autoprove forcing-logic.proofp-of-build.multi-assoc-expansion
(%autoinduct build.multi-assoc-expansion)
(%restrict default build.multi-assoc-expansion (equal as 'as)))
(%autoadmit build.multi-assoc-expansion-okp)
(local (%enable default build.multi-assoc-expansion-okp))
(%autoprove booleanp-of-build.multi-assoc-expansion-okp)
(%autoprove build.multi-assoc-expansion-okp-of-logic.appeal-identity)
(%autoprove lemma-1-for-soundness-of-build.multi-assoc-expansion-okp)
(%autoprove lemma-2-for-soundness-of-build.multi-assoc-expansion-okp)
(%autoprove forcing-soundness-of-build.multi-assoc-expansion-okp
(%enable default
lemma-1-for-soundness-of-build.multi-assoc-expansion-okp
lemma-2-for-soundness-of-build.multi-assoc-expansion-okp)
(%use (%instance (%thm forcing-logic.provablep-when-logic.proofp)
(x (build.multi-assoc-expansion (logic.provable-witness
(logic.conclusion (car (logic.subproofs x)))
axioms thms atbl)
(logic.extras x)))))))
(%autoadmit build.rev-disjunction)
(%autoadmit build.disjoined-rev-disjunction)
(%autoadmit build.disjoined-subset)
(%autoadmit build.all-superset-of-some)
(%autoprove forcing-logic.appeal-listp-of-build.all-superset-of-some
(%cdr-induction x)
(%restrict default build.all-superset-of-some (equal x 'x))
(%enable default build.disjoined-subset))
(%autoprove forcing-logic.strip-conclusions-of-build.all-superset-of-some
(%cdr-induction x)
(%restrict default build.all-superset-of-some (equal x 'x))
(%enable default build.disjoined-subset))
(%autoprove forcing-logic.proof-listp-of-build.all-superset-of-some
(%cdr-induction x)
(%restrict default build.all-superset-of-some (equal x 'x))
(%enable default build.disjoined-subset))
|
