<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E5">Th4</font></span>: <a NAME="T4"><span class="comment"><font color="firebrick">:: MESFUN12:4</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</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">A</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> holds <br/> (  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="mesfun12.html#K1" title="MESFUN12:func.1">chi</a> (<font color="Olive" title="b3">r</font>,<font color="Olive" title="b2">A</font>,<font color="Olive" title="b1">X</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Olive" title="b3">r</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp;  <a href="mesfun12.html#K1" title="MESFUN12:func.1">chi</a> (<font color="Olive" title="b3">r</font>,<font color="Olive" title="b2">A</font>,<font color="Olive" title="b1">X</font>) is <a href="mesfunc5.html#V4" title="MESFUNC5:attr.4">V121</a>() &amp;  <a href="mesfun12.html#K1" title="MESFUN12:func.1">chi</a> (<font color="Olive" title="b3">r</font>,<font color="Olive" title="b2">A</font>,<font color="Olive" title="b1">X</font>) is <a href="mesfunc5.html#V3" title="MESFUNC5:attr.3">V120</a>() )</div></div>
