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; This total order book, put together by Matt Kaufmann, is culled from events
; contributed by Pete Manolios and also benefits from contributions by Rob
; Sumners.
(in-package "ACL2")
(defun << (x y)
(declare (xargs :guard t))
(and (lexorder x y)
(not (equal x y))))
(defthm <<-irreflexive
(not (<< x x)))
(defthm <<-transitive
(implies (and (<< x y)
(<< y z))
(<< x z)))
(defthm <<-asymmetric
(implies (<< x y)
(not (<< y x))))
(defthm <<-trichotomy
(implies (and (not (<< y x))
(not (equal x y)))
(<< x y)))
(defthm <<-implies-lexorder
(implies (<< x y)
(lexorder x y)))
(in-theory (disable <<))
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