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



<b>assume </b><a NAME="E1:34"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">p</font> <a href="finseq_4.html#R2" target="_self">just_once_values</a> <font color="Maroon">x</font>
 ;<br/>

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

<b>assume </b><a NAME="E2:34"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font> &amp; <font color="Maroon">k</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x</font> <a href="finseq_4.html#K5" target="_self">..</a> <font color="Maroon">p</font> &amp; <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 ;<br/>

<a NAME="E3:34"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:34"/><b>then </b>
( <font color="Maroon">p</font> <a href="finseq_4.html#K1" target="_self">&lt;-</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="finseq_4.html#K5" target="_self">..</a> <font color="Maroon">p</font> &amp; <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="finseq_4.html#K5" target="_self">..</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E5:34"/>
contradiction
 <b>by </b><i>, , </i>;<br/>


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