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

<b>consider </b><font color="Maroon">c</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C</font>;<br/>
<a NAME="E2:8_1_1"/>
 <a href="xboole_0.html#K1">{}</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/>
<a NAME="E3:8_1_1"/><b>then </b>
 <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="classes1.html#D1">CLASSES1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:8_1_1"/>
not  <a href="cohsp_1.html#K2" target="_self">Sub_of_Fin</a> <font color="Maroon">C</font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i/>;<br/>

<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="classes1.html#D1">CLASSES1:def 1</a><br/>

<b>assume </b><a NAME="E5:8_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K2" target="_self">Sub_of_Fin</a> <font color="Maroon">C</font>
 ;<br/>

<a NAME="E6:8_1_1"/><b>then </b><i><font color="Green">E26</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">a</font> is <a href="finset_1.html#V1">finite</a> )
 
<b>by </b><i/>;<br/>
<b>assume </b><a NAME="E7:8_1_1"/>
<font color="Maroon">b</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a</font>
 ;<br/>

<a NAME="E8:8_1_1"/><b>then </b>
( <font color="Maroon">b</font> is <a href="finset_1.html#V1">finite</a> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> )
 
<b>by </b><i>, <a class="ref" href="classes1.html#D1">CLASSES1:def 1</a>, <a class="ref" href="finset_1.html#T13">FINSET_1:13</a></i>;<br/>
<b>hence </b><a NAME="E9:8_1_1"/>
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K2" target="_self">Sub_of_Fin</a> <font color="Maroon">C</font>
 <b>by </b><i/>;<br/>


</div>
