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

<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>given </b><font color="Maroon">k</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><a NAME="E1:96"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K2" target="_self">Seg</a> <font color="Maroon">k</font>
 ;<br/>

<b>thus </b><a NAME="E2:96"/>
(  <a href="finseq_1.html#K14" target="_self">Sgm</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="96_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:96_1"/>
 <a href="finseq_1.html#K14" target="_self">Sgm</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>hence </b><font color="Maroon">X</font> = 
 <a href="relat_1.html#K2">rng</a> <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i>, </i>
<br/>.= 
 <a href="xboole_0.html#K1">{}</a> 

;<br/><br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E3:96"/>
<font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E4:96"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14" target="_self">Sgm</a> <font color="Maroon">X</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:96"/><b>then </b>
 <a href="finseq_1.html#K4" target="_self">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14" target="_self">Sgm</a> <font color="Maroon">X</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2" target="_self">Seg</a> 0
 
<b>by </b><i>, <a class="ref" href="relat_1.html#T65">RELAT_1:65</a></i>;<br/>
<a NAME="E6:96"/><b>then </b>
 <a href="finseq_1.html#K3" target="_self">len</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14" target="_self">Sgm</a> <font color="Maroon">X</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E7:96"/>
 <a href="finseq_1.html#K14" target="_self">Sgm</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i/>;<br/>


</div>
