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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 "pequal-list-2-basic")
(include-book "pequal-list-2-rhses")
(include-book "pequal-list-2-lhses")
(%interactive)
(defthm forcing-equal-of-logic.pequal-list-rewrite-alt
;; BOZO add this to the ACL2 model?
(implies (and (force (equal (len x) (len y)))
(force (logic.term-listp x))
(force (logic.term-listp y)))
(equal (equal z (logic.pequal-list x y))
(and (true-listp z)
(logic.formula-listp z)
(logic.all-atomicp z)
(equal (list-fix x) (logic.=lhses z))
(equal (list-fix y) (logic.=rhses z))))))
(%autoprove forcing-logic.pequal-list-of-logic.=lhses-and-logic.=rhses
(%cdr-induction x))
(%autoprove forcing-equal-of-logic.pequal-list-rewrite
(%cdr-cdr-cdr-induction x y z))
(%autoprove forcing-equal-of-logic.pequal-list-rewrite-alt
(%use (%instance (%thm forcing-equal-of-logic.pequal-list-rewrite))))
(%autoprove logic.pequal-list-of-app-with-repeat
(%cdr-induction x))
(%ensure-exactly-these-rules-are-missing "../../logic/pequal-list")
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