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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 "eqtrace-okp")
(include-book "transitivity-eqtraces")
(include-book "../../clauses/basic-bldrs")
(set-verify-guards-eagerness 2)
(set-case-split-limitations nil)
(set-well-founded-relation ord<)
(set-measure-function rank)
(defund rw.trans1-eqtrace-bldr (x box proofs)
(declare (xargs :guard (and (rw.eqtracep x)
(rw.hypboxp box)
(rw.trans1-eqtrace-okp x)
(rw.eqtrace-okp x box)
(logic.appeal-listp proofs)
(equal (logic.strip-conclusions proofs) (rw.eqtrace-formula-list (rw.eqtrace->subtraces x) box)))
:verify-guards nil)
(ignore box))
(if (rw.eqtrace->iffp x)
(let ((proof1 (if (rw.eqtrace->iffp (first (rw.eqtrace->subtraces x)))
(first proofs)
(build.disjoined-iff-from-equal (first proofs))))
(proof2 (if (rw.eqtrace->iffp (second (rw.eqtrace->subtraces x)))
(second proofs)
(build.disjoined-iff-from-equal (second proofs)))))
(build.disjoined-transitivity-of-iff proof1 proof2))
(build.disjoined-transitivity-of-equal (first proofs) (second proofs))))
(defobligations rw.trans1-eqtrace-bldr
(build.disjoined-iff-from-equal
build.disjoined-transitivity-of-equal
build.disjoined-transitivity-of-iff))
(defthmd lemma-1-for-forcing-logic.appealp-of-rw.trans1-eqtrace-bldr
(implies (and (equal (logic.strip-conclusions proofs) (rw.eqtrace-formula-list x box))
(force (consp x)))
(equal (logic.conclusion (car proofs))
(rw.eqtrace-formula (car x) box))))
(defthmd lemma-2-for-forcing-logic.appealp-of-rw.trans1-eqtrace-bldr
(implies (and (equal (logic.strip-conclusions proofs) (rw.eqtrace-formula-list x box))
(force (consp (cdr x))))
(equal (logic.conclusion (second proofs))
(rw.eqtrace-formula (second x) box))))
(defthmd lemma-3-for-forcing-logic.appealp-of-rw.trans1-eqtrace-bldr
(implies (equal (logic.strip-conclusions proofs) (rw.eqtrace-formula-list x box))
(equal (consp proofs)
(consp x))))
(defthmd lemma-4-for-forcing-logic.appealp-of-rw.trans1-eqtrace-bldr
(implies (equal (logic.strip-conclusions proofs) (rw.eqtrace-formula-list x box))
(equal (consp (cdr proofs))
(consp (cdr x)))))
(encapsulate
()
(local (in-theory (enable rw.eqtrace-formula
rw.trans1-eqtrace-bldr
rw.trans1-eqtrace-okp
lemma-1-for-forcing-logic.appealp-of-rw.trans1-eqtrace-bldr
lemma-2-for-forcing-logic.appealp-of-rw.trans1-eqtrace-bldr
lemma-3-for-forcing-logic.appealp-of-rw.trans1-eqtrace-bldr
lemma-4-for-forcing-logic.appealp-of-rw.trans1-eqtrace-bldr)))
(defthm forcing-rw.trans1-eqtrace-bldr-under-iff
(iff (rw.trans1-eqtrace-bldr x box proofs)
t))
(defthm forcing-logic.appealp-of-rw.trans1-eqtrace-bldr
(implies (force (and (rw.eqtracep x)
(rw.hypboxp box)
(rw.trans1-eqtrace-okp x)
(rw.eqtrace-okp x box)
(logic.appeal-listp proofs)
(equal (logic.strip-conclusions proofs) (rw.eqtrace-formula-list (rw.eqtrace->subtraces x) box))))
(equal (logic.appealp (rw.trans1-eqtrace-bldr x box proofs))
t)))
(defthm forcing-logic.conclusion-of-rw.trans1-eqtrace-bldr
(implies (force (and (rw.eqtracep x)
(rw.hypboxp box)
(rw.trans1-eqtrace-okp x)
(rw.eqtrace-okp x box)
(logic.appeal-listp proofs)
(equal (logic.strip-conclusions proofs) (rw.eqtrace-formula-list (rw.eqtrace->subtraces x) box))))
(equal (logic.conclusion (rw.trans1-eqtrace-bldr x box proofs))
(rw.eqtrace-formula x box)))
:rule-classes ((:rewrite :backchain-limit-lst 0)))
(defthm@ forcing-logic.proofp-of-rw.trans1-eqtrace-bldr
(implies (force (and (rw.eqtracep x)
(rw.hypboxp box)
(rw.trans1-eqtrace-okp x)
(rw.eqtrace-okp x box)
(logic.appeal-listp proofs)
(equal (logic.strip-conclusions proofs) (rw.eqtrace-formula-list (rw.eqtrace->subtraces x) box))
;; ---
(logic.proof-listp proofs axioms thms atbl)
(equal (cdr (lookup 'iff atbl)) 2)
(@obligations rw.trans1-eqtrace-bldr)))
(equal (logic.proofp (rw.trans1-eqtrace-bldr x box proofs) axioms thms atbl)
t)))
(verify-guards rw.trans1-eqtrace-bldr))
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