<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span>   defines <a href="exchsort.html#V5" title="EXCHSORT:attr.5">ascending</a> <a onclick="hs(this)" href="javascript:()">EXCHSORT:def 10 : <br/></a><span> for <font color="Olive" title="b1">O</font> being    <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> <br/>  for <font color="Olive" title="b2">A</font> being   <a href="exchsort.html#NM3" title="EXCHSORT:NM.3">array</a> of <font color="Olive" title="b1">O</font> holds <br/> ( <font color="Olive" title="b2">A</font> is  <a href="exchsort.html#V5" title="EXCHSORT:attr.5">ascending</a>  iff  for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a>  st <font color="Olive" title="b3">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b2">A</font> &amp; <font color="Olive" title="b4">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b2">A</font> &amp; <font color="Olive" title="b3">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">b</font> holds <br/><font color="Olive" title="b2">A</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b3">a</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b2">A</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b4">b</font> );<br/></span></div>
