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<b>let </b><font color="Maroon">f</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:23"/><i><font color="Green">E30</font></i>: 
not  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font> is <a href="realset1.html#V1">trivial</a>
 <b>and </b><br/><a NAME="E2:23"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">f</font> is <a href="realset1.html#V1">trivial</a>
 ;<br/>

<b>consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:23"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i>, , <a class="ref" href="realset1.html#D4">REALSET1:def 4</a>, <a class="ref" href="relat_1.html#T60">RELAT_1:60</a></i>;<br/>
<a NAME="E5:23"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>then consider </b><font color="Maroon">y1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">y2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E7:23"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y1</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i><a class="ref" href="relat_1.html#D1">RELAT_1:def 1</a></i>;<br/>
<a NAME="E8:23"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y2</font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i>, , <a class="ref" href="relat_1.html#T23">RELAT_1:23</a></i>;<br/>
<b>hence </b><a NAME="E9:23"/>
contradiction
 <b>by </b><i/>;<br/>


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