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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:8"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>and </b><br/><a NAME="E2:8"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">n</font> <a href="finseq_2.html#K4">-tuples_on</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:8"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">n</font> <a href="finseq_2.html#K4">-tuples_on</a> <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon">s</font> being    <a href="finseq_2.html#M2">Element</a> of <a href="xboole_0.html#K1">{}</a>  <a href="finseq_2.html#K3">*</a> <b> such that </b><br/><a NAME="E6:8"/><i><font color="Green">E52</font></i>: 
( <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> )
 <b>by </b><i/>;<br/>
<a NAME="E7:8"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">s</font> <a href="tarski.html#R1">c=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<a NAME="E8:8"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/>
<a NAME="E9:8"/><b>then </b>
<font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T64">RELAT_1:64</a></i>;<br/>
<b>hence </b><a NAME="E10:8"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/>


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