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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 "eqtracep")
(set-verify-guards-eagerness 2)
(set-case-split-limitations nil)
(set-well-founded-relation ord<)
(set-measure-function rank)
(definlined rw.direct-iff-eqtrace (okp nhyp)
;; Try to generate a direct eqtrace from an nhyp.
;; The nhyp should have one of these forms:
;; -- (not* (iff lhs rhs))
;; -- (not* (iff rhs lhs))
;; Where lhs and rhs are distinct.
(declare (xargs :guard (logic.termp nhyp)))
(and okp
(clause.negative-termp nhyp)
(let ((guts (clause.negative-term-guts nhyp)))
(and (logic.functionp guts)
(equal (logic.function-name guts) 'iff)
(let ((args (logic.function-args guts)))
(and (equal (len args) 2)
(let ((lhs (first args))
(rhs (second args)))
(cond ((logic.term-< lhs rhs)
(rw.eqtrace 'direct-iff t lhs rhs nil))
((logic.term-< rhs lhs)
(rw.eqtrace 'direct-iff t rhs lhs nil))
(t
;; Lhs and rhs are not distinct. We would be
;; assuming lhs iff lhs, which is useless.
nil)))))))))
(encapsulate
()
(local (in-theory (enable rw.direct-iff-eqtrace)))
(defthm forcing-rw.eqtrace->method-of-rw.direct-iff-eqtrace
(implies (force (rw.direct-iff-eqtrace okp nhyp))
(equal (rw.eqtrace->method (rw.direct-iff-eqtrace okp nhyp))
'direct-iff)))
(defthm forcing-rw.eqtrace->iffp-of-rw.direct-iff-eqtrace
(implies (force (rw.direct-iff-eqtrace okp nhyp))
(equal (rw.eqtrace->iffp (rw.direct-iff-eqtrace okp nhyp))
t)))
(defthm forcing-rw.eqtrace->subtraces-of-rw.direct-iff-eqtrace
(implies (force (rw.direct-iff-eqtrace okp nhyp))
(equal (rw.eqtrace->subtraces (rw.direct-iff-eqtrace okp nhyp))
nil)))
(defthm forcing-rw.eqtracep-of-rw.direct-iff-eqtrace
(implies (force (and (rw.direct-iff-eqtrace okp nhyp)
(logic.termp nhyp)))
(equal (rw.eqtracep (rw.direct-iff-eqtrace okp nhyp))
t)))
(defthm forcing-rw.eqtrace-atblp-of-rw.direct-iff-eqtrace
(implies (force (and (rw.direct-iff-eqtrace okp nhyp)
(logic.termp nhyp)
(logic.term-atblp nhyp atbl)))
(equal (rw.eqtrace-atblp (rw.direct-iff-eqtrace okp nhyp) atbl)
t)))
(defthm rw.direct-iff-eqtrace-normalize-okp-1
(implies (and (rw.direct-iff-eqtrace okp nhyp)
(syntaxp (not (equal okp ''t))))
(equal (rw.direct-iff-eqtrace okp nhyp)
(rw.direct-iff-eqtrace t nhyp))))
(defthm rw.direct-iff-eqtrace-normalize-okp-2
(implies (not (rw.direct-iff-eqtrace t nhyp))
(equal (rw.direct-iff-eqtrace okp nhyp)
nil)))
(defthm rw.direct-iff-eqtrace-normalize-okp-3
(equal (rw.direct-iff-eqtrace nil nhyp)
nil)))
(defund rw.find-nhyp-for-direct-iff-eqtracep (nhyps x)
;; Find the first nhyp in a list that would generate this direct-iff eqtrace.
(declare (xargs :guard (and (logic.term-listp nhyps)
(rw.eqtracep x))))
(if (consp nhyps)
(if (equal (rw.direct-iff-eqtrace t (car nhyps)) x)
(car nhyps)
(rw.find-nhyp-for-direct-iff-eqtracep (cdr nhyps) x))
nil))
(encapsulate
()
(local (in-theory (enable rw.find-nhyp-for-direct-iff-eqtracep)))
(defthm rw.find-nhyp-for-direct-iff-eqtracep-of-nil
(equal (rw.find-nhyp-for-direct-iff-eqtracep nil x)
nil))
(defthm forcing-logic.termp-of-rw.find-nhyp-for-direct-iff-eqtracep
(implies (force (and (rw.find-nhyp-for-direct-iff-eqtracep nhyps x)
(logic.term-listp nhyps)))
(equal (logic.termp (rw.find-nhyp-for-direct-iff-eqtracep nhyps x))
t)))
(defthm forcing-logic.term-atblp-of-rw.find-nhyp-for-direct-iff-eqtracep
(implies (force (and (rw.find-nhyp-for-direct-iff-eqtracep nhyps x)
(logic.term-list-atblp nhyps atbl)))
(equal (logic.term-atblp (rw.find-nhyp-for-direct-iff-eqtracep nhyps x) atbl)
t)))
(defthm forcing-memberp-of-rw.find-nhyp-for-direct-iff-eqtracep
(implies (force (rw.find-nhyp-for-direct-iff-eqtracep nhyps x))
(equal (memberp (rw.find-nhyp-for-direct-iff-eqtracep nhyps x) nhyps)
t)))
(defthm forcing-rw.direct-iff-eqtrace-of-rw.find-nhyp-for-direct-iff-eqtracep
(implies (force (rw.find-nhyp-for-direct-iff-eqtracep nhyps x))
(equal (rw.direct-iff-eqtrace t (rw.find-nhyp-for-direct-iff-eqtracep nhyps x))
x))))
(defund rw.direct-iff-eqtrace-okp (x box)
;; Check if any nhyp in the hypbox would generate this direct-iff eqtrace.
(declare (xargs :guard (and (rw.eqtracep x)
(rw.hypboxp box))))
(and (equal (rw.eqtrace->method x) 'direct-iff)
(equal (rw.eqtrace->iffp x) t)
(if (or (rw.find-nhyp-for-direct-iff-eqtracep (rw.hypbox->left box) x)
(rw.find-nhyp-for-direct-iff-eqtracep (rw.hypbox->right box) x))
t
nil)))
(encapsulate
()
(local (in-theory (enable rw.direct-iff-eqtrace-okp)))
(defthm booleanp-of-rw.direct-iff-eqtrace-okp
(equal (booleanp (rw.direct-iff-eqtrace-okp x box))
t)
:hints(("Goal" :in-theory (disable forcing-booleanp-of-rw.eqtrace->iffp))))
(defthmd lemma-for-forcing-rw.direct-iff-eqtrace-okp-rw.direct-iff-eqtrace
(implies (and (memberp nhyp nhyps)
(rw.direct-iff-eqtrace okp nhyp))
(iff (rw.find-nhyp-for-direct-iff-eqtracep nhyps (rw.direct-iff-eqtrace okp nhyp))
nhyp))
:hints(("Goal" :in-theory (enable rw.find-nhyp-for-direct-iff-eqtracep))))
(defthm forcing-rw.direct-iff-eqtrace-okp-rw.direct-iff-eqtrace
(implies (force (and (rw.direct-iff-eqtrace okp nhyp)
(or (memberp nhyp (rw.hypbox->left box))
(memberp nhyp (rw.hypbox->right box)))))
(equal (rw.direct-iff-eqtrace-okp (rw.direct-iff-eqtrace okp nhyp) box)
t))
:hints(("Goal" :in-theory (e/d (lemma-for-forcing-rw.direct-iff-eqtrace-okp-rw.direct-iff-eqtrace)
(rw.direct-iff-eqtrace-normalize-okp-1))))))
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