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<b>let </b><font color="Maroon" title="c1">f</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:22"/><i><font color="Green" title="E19">A1</font></i>: 
not  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">f</font> is <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a>
 <b>and </b><br/><a NAME="E2:22"/><i><font color="Green" title="E20">A2</font></i>: 
<font color="Maroon" title="c1">f</font> is <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a>
 ;<br/>

<b>consider </b><font color="Maroon" title="c2">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:22"/><i><font color="Green" title="E21">A3</font></i>: 
<font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="finseq_6.html#E1:22"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="finseq_6.html#E2:22"><i><font color="Green" title="E20">A2</font></i></a>, <a class="ref" href="realset1.html#D4" title="REALSET1:def.4">REALSET1:def 4</a>, <a class="ref" href="relat_1.html#T60" title="RELAT_1:th.60">RELAT_1:60</a></i>;<br/>
<a NAME="E5:22"/>
<font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">f</font>
 
<b>by </b><i><a class="txt" href="finseq_6.html#E4:22"><i><font color="Green" title="E21">A3</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c3">y1</font>, <font color="Maroon" title="c4">y2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E7:22"/><i><font color="Green" title="E22">A4</font></i>: 
<font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="ref" href="relat_1.html#D1" title="RELAT_1:def.1">RELAT_1:def 1</a></i>;<br/>
<a NAME="E8:22"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">y2</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="finseq_6.html#E4:22"><i><font color="Green" title="E21">A3</font></i></a>, <a class="txt" href="finseq_6.html#E7:22"><i><font color="Green" title="E22">A4</font></i></a>, <a class="ref" href="relat_1.html#T23" title="RELAT_1:th.23">RELAT_1:23</a></i>;<br/>
<b>hence </b><a NAME="E9:22"/>
contradiction
 <b>by </b><i><a class="txt" href="finseq_6.html#E1:22"><i><font color="Green" title="E19">A1</font></i></a></i>;<br/>


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