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<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">Y</font> be  <a href="finset_1.html#V1">finite</a> <a href="setfam_1.html#NM1">Subset-Family</a> of <font color="Maroon">X</font>;<br/>



<b>assume </b><a NAME="E1:31"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">Y</font> is <a href="yellow15.html#V1" target="_self">in_general_position</a>
 ;<br/>

<a NAME="E2:31"/><i><font color="Green">E32</font></i>: 
 <a href="setfam_1.html#K5">union</a> <span class="p1">(<span class="default"><a href="yellow15.html#K2" target="_self">Components</a> <font color="Maroon">Y</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:31"/>
for <font color="Olive">A</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>  st <font color="Olive">A</font> <a href="hidden.html#R2">in</a>  <a href="yellow15.html#K2" target="_self">Components</a> <font color="Maroon">Y</font> holds <br/>( <font color="Olive">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; ( for <font color="Olive">B</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>  holds <br/>(  not <font color="Olive">B</font> <a href="hidden.html#R2">in</a>  <a href="yellow15.html#K2" target="_self">Components</a> <font color="Maroon">Y</font> or <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <font color="Olive">B</font> or <font color="Olive">A</font> <a href="xboole_0.html#R1">misses</a> <font color="Olive">B</font> ) ) )
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E4:31"/>
 <a href="yellow15.html#K2" target="_self">Components</a> <font color="Maroon">Y</font> is    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">X</font>
 <b>by </b><i>, <a class="ref" href="eqrel_1.html#D6">EQREL_1:def 6</a></i>;<br/>


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