<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span>   defines <a href="armstrng.html#V11" title="ARMSTRNG:attr.11">without_proper_subsets</a> <a onclick="hs(this)" href="javascript:()">ARMSTRNG:def 27 : <br/></a><span> for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds <br/> ( <font color="Olive" title="b1">X</font> is  <a href="armstrng.html#V11" title="ARMSTRNG:attr.11">without_proper_subsets</a>  iff  for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b2">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">X</font> &amp; <font color="Olive" title="b3">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">X</font> &amp; <font color="Olive" title="b2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">y</font> holds <br/><font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">y</font> );<br/></span></div>
