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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:26"/><i><font color="Green">E8</font></i>: 
not  <a href="margrel1.html#K4" target="_self">empty_rel</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>2</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="margrel1.html#K4" target="_self">empty_rel</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E3:26"/>
 <a href="margrel1.html#K4" target="_self">empty_rel</a> <font color="Maroon">c<sub>1</sub></font> is   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="finseq_1.html#K13">*</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="margrel1.html#D8" target="_self">Def8</a></i>;<br/>
<a NAME="E4:26"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="finseq_1.html#K13">*</a> 
 
<b>by </b><i><a class="txt" href="margrel1.html#E1:26"><i><font color="Green">E8</font></i></a>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/>
<a NAME="E6:26"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="margrel1.html#K4" target="_self">empty_rel</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="margrel1.html#E1:26"><i><font color="Green">E8</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:26"/>
contradiction
 <b>by </b><i><a class="ref" href="margrel1.html#D10" target="_self">Def10</a></i>;<br/>


</div>
