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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 "primitives-3")
(%interactive)
;; Equalities with Sums.
(%autoprove |(= a (+ a b))|
(%enable default nfix)
(%disable default |[OUTSIDE](< a (+ a b))|)
(%auto)
(%use (%thm |(< a (+ a b))|))
(%auto :strategy (cleanup split crewrite)))
(%autoprove |(= a (+ b a))|)
(%autoprove |lemma for (= (+ a b) (+ a c))|
(%use (%instance (%thm |(< (+ a b) (+ a c))|) (a a) (b b) (c c)))
(%use (%instance (%thm |(< (+ a b) (+ a c))|) (a a) (b c) (c b)))
(%disable default |[OUTSIDE](< (+ a b) (+ a c))|)
(%disable default |(< (+ a b) (+ a c))|))
(%autoprove |(= (+ a b) (+ a c))|
(%enable default nfix)
(%use (%instance (%thm |lemma for (= (+ a b) (+ a c))|)
(a a)
(b (nfix b))
(c (nfix c)))))
(%autoprove |(= (+ a b) (+ c a))|)
(%autoprove |(= (+ b a) (+ c a))|)
(%autoprove |(= (+ b a) (+ a c))|)
(%autoprove |(= 0 (+ a b))|
(%use (%instance (%thm |(< (+ a b) (+ a c))|) (a b) (b 0) (c a)))
(%disable default
|(< (+ a b) (+ a c))|
|[OUTSIDE](< (+ a b) (+ a c))|)
(%auto :strategy (cleanup split crewrite)))
(%autoprove |lemma for (= (+ a x b) (+ c x d))|)
(%autoprove |(= (+ a x b) (+ c x d))|
(%use (%instance (%thm |lemma for (= (+ a x b) (+ c x d))|)
(e a) (b x) (c b) (d c) (f d))))
(%autoprove squeeze-law-one
(%enable default nfix))
(%autoprove squeeze-law-two
(%enable default nfix))
(%autoprove squeeze-law-three
(%enable default nfix))
|
