<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">T</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">F</font> be   <a href="setfam_1.html#NM1">Subset-Family</a> of <font color="Maroon">T</font>;<br/>



<b>assume </b><a NAME="E1:23"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">F</font> is   <a href="prob_1.html#NM3">SigmaField</a> of <font color="Maroon">T</font>
 ;<br/>

<b>let </b><font color="Maroon">G</font> be  <a href="card_4.html#V1">countable</a> <a href="setfam_1.html#NM1">Subset-Family</a> of <font color="Maroon">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="topgen_4.html#D4" target="_self">TOPGEN_4:def 4</a><br/>

<b>assume </b><a NAME="E2:23"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">G</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">F</font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:23_1"/>
( <font color="Maroon">G</font> is <a href="xboole_0.html#V1">empty</a> or  not <font color="Maroon">G</font> is <a href="xboole_0.html#V1">empty</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_1_1"><b>suppose </b></a><a NAME="E1:23_1_1"/>
<font color="Maroon">G</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:23_1_1"/>
 <a href="setfam_1.html#K5">union</a> <font color="Maroon">G</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 <b>by </b><i>, <a class="ref" href="prob_1.html#T10">PROB_1:10</a>, <a class="ref" href="zfmisc_1.html#T2">ZFMISC_1:2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_1_2"><b>suppose </b></a><a NAME="E1:23_1_2"/>
not <font color="Maroon">G</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:23_1_2"/>
 <a href="setfam_1.html#K5">union</a> <font color="Maroon">G</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 <b>by </b><i>, , <a class="ref" href="measure1.html#D9">MEASURE1:def 9</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
