<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span>   defines <a href="filter_2.html#R1" title="FILTER_2:pred.1">=</a> <a onclick="hs(this)" href="javascript:()">FILTER_2:def 1 : <br/></a><span> for <font color="Olive" title="b1">D</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">X1</font>, <font color="Olive" title="b3">X2</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">D</font> holds <br/> ( <font color="Olive" title="b2">X1</font> <a href="filter_2.html#R1" title="FILTER_2:pred.1">=</a> <font color="Olive" title="b3">X2</font> iff  for <font color="Olive" title="b4">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">D</font> holds <br/> ( <font color="Olive" title="b4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">X1</font> iff <font color="Olive" title="b4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">X2</font> ) );<br/></span></div>
