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

<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">A</font> be    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">D</font>;<br/>







<b>assume </b><a NAME="E1:24"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E2:24"/><i><font color="Green">E29</font></i>: 
<span class="p1">(<span class="default"><a href="borsuk_1.html#K2" target="_self">proj</a> <font color="Maroon">D</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E3:24"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K2" target="_self">proj</a> <font color="Maroon">D</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:24"/><b>then </b>
not <span class="p1">(<span class="default"><a href="borsuk_1.html#K2" target="_self">proj</a> <font color="Maroon">D</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#T4" target="_self">Th4</a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>
<b>hence </b><a NAME="E5:24"/>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K2" target="_self">proj</a> <font color="Maroon">D</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="borsuk_1.html#T5" target="_self">Th5</a>, <a class="ref" href="eqrel_1.html#D6">EQREL_1:def 6</a></i>;<br/>


</div>
