<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">U0</font> be   <a href="unialg_1.html#NM2">Universal_Algebra</a>;<br/><b>let </b><font color="Maroon">H</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="unialg_3.html#K1" target="_self">Sub</a> <font color="Maroon">U0</font></span>)</span>;<br/>



<b>consider </b><font color="Maroon">u</font> being    <a href="unialg_3.html#M2" target="_self">Element</a> of  <a href="unialg_3.html#K1" target="_self">Sub</a> <font color="Maroon">U0</font><b> such that </b><br/><a NAME="E2:17"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="subset_1.html#T10">SUBSET_1:10</a></i>;<br/>
<a NAME="E3:17"/>
<span class="p1">(<span class="default"><a href="unialg_3.html#K6" target="_self">Carr</a> <font color="Maroon">U0</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="unialg_3.html#K6" target="_self">Carr</a> <font color="Maroon">U0</font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">H</font>
 
<b>by </b><i>, <a class="ref" href="funct_2.html#T43">FUNCT_2:43</a></i>;<br/>
<b>hence </b><a NAME="E4:17"/>
not <span class="p1">(<span class="default"><a href="unialg_3.html#K6" target="_self">Carr</a> <font color="Maroon">U0</font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">H</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>


</div>
