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

<b>let </b><font color="Maroon">v</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a> ;<br/>

<b>assume </b><a NAME="E1:31"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">v</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>assume </b><a NAME="E2:31"/>
 <a href="goboard2.html#K2" target="_self">Incr</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E3:31"/><b>then </b>
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" target="_self">Incr</a> <font color="Maroon">v</font></span>)</span> <a href="hidden.html#R1">=</a> 0 &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K2" target="_self">Incr</a> <font color="Maroon">v</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">v</font></span>)</span> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">v</font> is <a href="finset_1.html#V1">finite</a> )
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/>
<a NAME="E4:31"/><b>then </b>
(  <a href="relat_1.html#K2">rng</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">v</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="card_2.html#T59">CARD_2:59</a>, <a class="ref" href="finseq_1.html#T27">FINSEQ_1:27</a></i>;<br/>
<b>hence </b><a NAME="E5:31"/>
contradiction
 ;<br/>


</div>
