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

<b>let </b><font color="Maroon">P</font> be    <a href="pua2mss1.html#M2" target="_self">IndexedPartition</a> of <font color="Maroon">X</font>;<br/>

<b>thus </b><a NAME="E1:27_1_1"/>
<font color="Maroon">P</font> is <a href="funct_1.html#V2">one-to-one</a>
 <b>by </b><i/>;<br/>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_1.html#D15">FUNCT_1:def 15</a><br/>

<b>assume </b><a NAME="E2:27_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">P</font>
 ;<br/>

<a NAME="E3:27_1_1"/><b>then </b>
( <font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="pua2mss1.html#K3" target="_self">rng</a> <font color="Maroon">P</font> &amp;  <a href="pua2mss1.html#K3" target="_self">rng</a> <font color="Maroon">P</font> is    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">X</font> &amp; ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or <font color="Maroon">X</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  ) )
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E4:27_1_1"/>
not <font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i><a class="ref" href="eqrel_1.html#D6">EQREL_1:def 6</a></i>;<br/>


</div>
