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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:88"/>
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="tex_4.html#K3" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="tex_4.html#T34" target="_self">Th34</a></i>;<br/>
<a NAME="E2:88"/><b>then </b><i><font color="Green">E58</font></i>: 
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tex_4.html#K3" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T49">PRE_TOPC:49</a></i>;<br/>
<a NAME="E3:88"/>
 <a href="tex_4.html#K3" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="tex_4.html#T61" target="_self">Th61</a></i>;<br/>
<a NAME="E4:88"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tex_4.html#K3" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="tops_1.html#T31">TOPS_1:31</a></i>;<br/>
<b>hence </b><a NAME="E5:88"/>
 <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tex_4.html#K3" target="_self">MaxADSet</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="tex_4.html#E2:88"><i><font color="Green">E58</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


</div>
