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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-2")
(%interactive)
;; Less-Than and Addition.
(%autoprove |(< (+ a b) (+ a c))| (%use (build.axiom (axiom-less-than-of-plus-and-plus))))
(%autoprove |(< a (+ a b))|
(%disable default
|(< (+ a b) (+ a c))|
|[OUTSIDE](< (+ a b) (+ a c))|)
(%use (%instance (%thm |(< (+ a b) (+ a c))|) (b 0) (c b))))
(%autoprove |(< a (+ b a))|)
(%autoprove |(< (+ a b) a)|
(%disable default
|(< (+ a b) (+ a c))|
|[OUTSIDE](< (+ a b) (+ a c))|)
(%use (%instance (%thm |(< (+ a b) (+ a c))|) (c 0))))
(%autoprove |(< (+ b a) a)|)
(%autoprove |(< a (+ b c a))|)
(%autoprove |(< a (+ b a c))|)
(%autoprove |(< a (+ b c d a))|)
(%autoprove |(< a (+ b c a d))|)
(%autoprove |(< a (+ b c d e a))|)
(%autoprove |(< a (+ b c d a e))|)
(%autoprove |(< a (+ b c d e f a))|)
(%autoprove |(< a (+ b c d e a f))|)
(%autoprove |(< (+ a b) (+ c a))|)
(%autoprove |(< (+ b a) (+ c a))|)
(%autoprove |(< (+ b a) (+ a c))|)
(%autoprove |(< (+ a b) (+ c a d))|)
(%autoprove |(< (+ b a c) (+ d a))|)
(%autoprove |a <= b, c != 0 --> a < b+c| (%enable default zp))
(%autoprove |a <= b, c != 0 --> a < c+b|)
(%autoprove |a <= b, c != 0 --> a < c+b+d|
;; BOZO, why do I have to disable this?
(%disable default [OUTSIDE]LESS-OF-ZERO-LEFT))
(%autoprove |a <= b, c != 0 --> a < c+d+b|
(%disable default [OUTSIDE]LESS-OF-ZERO-LEFT))
(%autoprove |c < a, d <= b --> c+d < a+b|
(%use (%instance (%thm transitivity-of-<-three) (a (+ c d)) (b (+ c b)) (c (+ a b)))))
(%autoprove |c < a, d <= b --> c+d < b+a|)
(%autoprove |c <= a, d < b --> c+d < a+b|
(%use (%instance (%thm |c < a, d <= b --> c+d < a+b|) (c d) (a b) (d c) (b a))))
(%autoprove |c <= a, d < b --> c+d < b+a|)
(%autoprove |c <= a, d <= b --> c+d <= a+b|
(%use (%instance (%thm transitivity-of-<-four) (a (+ c d)) (b (+ c b)) (c (+ a b)))))
(%autoprove |c <= a, d <= b --> c+d <= b+a|)
|
