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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 "proofp-2")
(%interactive)
(%defchoose logic.provable-witness proof (x axioms thms atbl)
(and (logic.appealp proof)
(logic.proofp proof axioms thms atbl)
(equal (logic.conclusion proof) x)))
(defun logic.provablep (x axioms thms atbl)
;; BOZO because we used defun-sk to introduce it, which is based on
;; ACL2::defun instead of MILAWA::defun, there's no syntax-defuns entry for
;; logic.provablep, So, we now add a redundant definition of logic.provablep
;; using MILAWA::defun, so that %autoadmit knows what its definition is.
(declare (xargs :guard (and (logic.formulap x)
(logic.formula-listp axioms)
(logic.formula-listp thms)
(logic.arity-tablep atbl))))
(let ((proof (logic.provable-witness x axioms thms atbl)))
(and (logic.appealp proof)
(logic.proofp proof axioms thms atbl)
(equal (logic.conclusion proof) x))))
(%autoadmit logic.provablep)
(%autoprove logic.provablep-suff
(%use (build.axiom (defchoose-axiom-for-logic.provable-witness)))
(%enable default logic.provablep))
(%autoprove booleanp-of-logic.provablep
(%enable default logic.provablep))
(%autoprove forcing-logic.appealp-of-logic.provable-witness
(%enable default logic.provablep))
(%autoprove forcing-logic.proofp-of-logic.provable-witness
(%enable default logic.provablep)
(%disable default forcing-logic.appealp-of-logic.provable-witness))
(%autoprove forcing-logic.conclusion-of-logic.provable-witness
(%enable default logic.provablep))
(%autoprove logic.formulap-when-logic.provablep
(%disable default forcing-logic.formulap-of-logic.conclusion)
(%use (%instance (%thm forcing-logic.formulap-of-logic.conclusion)
(x (logic.provable-witness x axioms thms atbl))))
;; This %split is important for some reason
(%split))
(%autoprove logic.formula-atblp-when-logic.provablep
(%use (%instance (%thm logic.formula-atblp-of-logic.conclusion-when-logic.proofp)
(x (logic.provable-witness x axioms thms atbl)))))
(%autoprove logic.provablep-when-not-consp
(%disable default logic.formulap-when-not-consp)
(%use (%instance (%thm logic.formulap-when-not-consp))))
(%autoprove forcing-logic.provablep-when-logic.proofp
(%use (%instance (%thm logic.provablep-suff)
(proof x)
(x (logic.conclusion x)))))
(%deflist logic.provable-listp (x axioms thms atbl)
(logic.provablep x axioms thms atbl))
(%autoprove logic.provablep-of-car-when-logic.provable-listp-free)
(%autoprove logic.provablep-of-second-when-logic.provable-listp)
(%autoprove forcing-logic.provable-listp-of-logic.strip-conclusions-when-logic.proof-listp
(%cdr-induction x))
(%autoprove forcing-logic.provable-listp-of-logic.subproofs-when-logic.proofp
(%restrict default definition-of-logic.proofp (equal x 'x)))
(%autoprove logic.formula-list-atblp-of-when-logic.provable-listp
(%cdr-induction x))
(%defprojection :list (logic.provable-list-witness x axioms thms atbl)
:element (logic.provable-witness x axioms thms atbl))
(%autoprove forcing-logic.appeal-listp-of-logic.provable-list-witness
(%cdr-induction x))
(%autoprove force-logic.proof-listp-of-logic.provable-list-witness
(%cdr-induction x))
(%autoprove forcing-logic.strip-conclusions-of-logic.provable-list-witness
(%cdr-induction x))
(%autoprove logic.provablep-of-logic.conclusion-of-first-when-logic.provable-listp)
(%autoprove logic.provablep-of-logic.conclusion-of-second-when-logic.provable-listp)
(%autoprove logic.provablep-of-logic.conclusion-of-third-when-logic.provable-listp)
(%autoprove logic.provablep-of-logic.conclusion-of-fourth-when-logic.provable-listp)
|
