File: _lt_.html

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<html>
<head><title>_lt_.html  --  ACL2 Version 3.1</title></head>
<body text=#000000 bgcolor="#FFFFFF">
<h2>&lt;</h2>less-than
<pre>Major Section:  <a href="PROGRAMMING.html">PROGRAMMING</a>
</pre><p>

Completion Axiom:

<pre>
(equal (&lt; x y)
       (if (and (rationalp x)
                (rationalp y))
           (&lt; x y)
         (let ((x1 (if (acl2-numberp x) x 0))
               (y1 (if (acl2-numberp y) y 0)))
           (or (&lt; (realpart x1) (realpart y1))
               (and (equal (realpart x1) (realpart y1))
                    (&lt; (imagpart x1) (imagpart y1)))))))
</pre>

<p>
<a href="GUARD.html">Guard</a> for <code>(&lt; x y)</code>:

<pre>
(and (rationalp x) (rationalp y))
</pre>

Notice that like all arithmetic functions, <code>&lt;</code> treats non-numeric
inputs as <code>0</code>.<p>

This function has the usual meaning on the rational numbers, but is
extended to the complex rational numbers using the lexicographic
order:  first the real parts are compared, and if they are equal,
then the imaginary parts are compared.
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</body>
</html>