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<b>let </b><font color="Maroon">f</font> be  <a href="cohsp_1.html#V8" target="_self">U-continuous</a> <a href="funct_1.html#NM1">Function</a>;<br/>

<b>assume </b><a NAME="E1:79"/><i><font color="Green">E26</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> is <a href="classes1.html#V1">subset-closed</a>
 ;<br/>

<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E2:79"/><i><font color="Green">E27</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K7" target="_self">Trace</a> <font color="Maroon">f</font>
 ;<br/>

<a NAME="E3:79"/><b>then </b><i><font color="Green">E36</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> &amp; ( for <font color="Olive">b</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">b</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> &amp; <font color="Olive">b</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">b</font> holds <br/><font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> ) )
 
<b>by </b><i><a class="ref" href="cohsp_1.html#T2" target="_self">Th2</a></i>;<br/>
<b>then consider </b><font color="Maroon">b</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:79"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">b</font> is <a href="finset_1.html#V1">finite</a> &amp; <font color="Maroon">b</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">b</font> )
 <b>by </b><i>, <a class="txt" href="cohsp_1.html#E2:79"><i><font color="Green">E27</font></i></a></i>;<br/>
<a NAME="E6:79"/>
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font>
 
<b>by </b><i>, <a class="txt" href="cohsp_1.html#E5:79"><i><font color="Green">E41</font></i></a>, , <a class="ref" href="classes1.html#D1">CLASSES1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E7:79"/>
<font color="Maroon">a</font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i>, , <a class="ref" href="cohsp_1.html#T2" target="_self">Th2</a></i>;<br/>


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