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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")
(%interactive)
(%autoadmit logic.functional-axiom)
(%autoprove forcing-logic.formulap-of-logic.functional-axiom
(%enable default logic.functional-axiom))
(%autoprove forcing-logic.formula-atblp-of-logic.functional-axiom
(%enable default logic.functional-axiom))
(%autoadmit logic.functional-axiom-alt1)
(defmacro %logic.functional-axiom-alt1-induction (ti si tacc sacc)
`(%induct (rank ,ti)
((or (not (consp ,ti))
(not (consp ,si)))
nil)
((and (consp ,ti)
(consp ,si))
(((,ti (cdr ,ti))
(,si (cdr ,si))
(,tacc (cons (car ,ti) ,tacc))
(,sacc (cons (car ,si) ,sacc)))))))
(%autoprove logic.check-functional-axiom-of-logic.functional-axiom-alt1
(%logic.functional-axiom-alt1-induction ti si tacc sacc)
(%restrict default logic.functional-axiom-alt1 (equal ti 'ti))
(%auto)
(%restrict default logic.check-functional-axiom (equal ti 'tacc)))
(%autoadmit logic.functional-axiom-alt2)
(%autoprove logic.functional-axiom-alt1/alt2-equivalence
;; broken with the alternate rewriter strategy withotu assms
;; (%skip) reverting
(%logic.functional-axiom-alt1-induction ti si tacc sacc)
(%restrict default logic.functional-axiom-alt1 (equal ti 'ti))
(%enable default logic.functional-axiom-alt2)
(%disable default
aggressive-equal-of-logic.pequals
aggressive-equal-of-logic.pors
aggressive-equal-of-logic.pnots
forcing-logic.formulap-of-logic.por
forcing-logic.formulap-of-logic.pequal
forcing-logic.formulap-of-logic.pnot
forcing-logic.formulap-of-logic.pequal-list
forcing-equal-of-logic.por-rewrite-two
forcing-equal-of-logic.por-rewrite
forcing-logic.fmtype-of-logic.disjoin-formulas
[outside]consp-of-logic.pequal-list ;; why ??
))
(%autoprove logic.functional-axiom-alt2/main-equivalence
(%disable default
forcing-logic.formulap-of-logic.pequal-list
logic.formula-listp-of-logic.negate-formulas
forcing-logic.termp-of-logic.function
forcing-equal-of-logic.pequal-list-rewrite
forcing-logic.formula-listp-of-app
forcing-logic.formulap-of-logic.pequal
equal-of-logic.pequal-list-and-logic.pequal-list
equal-of-logic.disjoin-formulas-and-logic.disjoin-formulas-when-same-len)
(%enable default
logic.functional-axiom-alt2
logic.functional-axiom))
(%autoprove forcing-logic.check-functional-axiom-of-logic.functional-axiom
(%use (%instance (%thm logic.check-functional-axiom-of-logic.functional-axiom-alt1)
(tacc nil)
(sacc nil))))
(%ensure-exactly-these-rules-are-missing "../../logic/functional-axiom")
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