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

<b>let </b><font color="Maroon">p</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/><b>let </b><font color="Maroon">A</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:64"/><i><font color="Green">E40</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="finseq_3.html#K1" target="_self">-</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font>
 ;<br/>

<b>assume </b><a NAME="E2:64"/>
<font color="Maroon">A</font> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font>
 ;<br/>

<a NAME="E3:64"/><b>then </b>
<font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T173">RELAT_1:173</a></i>;<br/>
<a NAME="E4:64"/><b>then </b>
( not <font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font>, <a href="xboole_0.html#K1">{}</a>  <a href="tarski.html#R2">are_equipotent</a>  &amp; <font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font> &amp;  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span> &amp;  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span> is <a href="finset_1.html#V1">finite</a> )
 
<b>by </b><i><a class="ref" href="card_1.html#T46">CARD_1:46</a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a>, <a class="ref" href="relat_1.html#T167">RELAT_1:167</a></i>;<br/>
<a NAME="E5:64"/><b>then </b>
( 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="card_1.html#T21">CARD_1:21</a>, <a class="ref" href="card_1.html#T78">CARD_1:78</a></i>;<br/>
<a NAME="E6:64"/><b>then </b>
( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="finseq_3.html#K1" target="_self">-</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="finseq_3.html#E1:64"><i><font color="Green">E40</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:64"/>
contradiction
 <b>by </b><i><a class="ref" href="finseq_3.html#T13" target="_self">Th13</a></i>;<br/>


</div>
