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<b>let </b><font color="Maroon" title="c1">A</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">S</font> be    <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c2">X</font>;<br/>





<b>assume </b><a NAME="E1:66"/><i><font color="Green" title="E33">A1</font></i>: 
<font color="Maroon" title="c1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">S</font>
 ;<br/>

<a NAME="E2:66"/><b>then </b>
not <font color="Maroon" title="c1">A</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 
<b>by </b><i><a class="ref" href="eqrel_1.html#D6" target="_self" title="EQREL_1:def.6">Def6</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:66"/><i><font color="Green" title="E34">A2</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">x</font>
;<br/>

<b>thus </b><a NAME="E5:66"/>
( <font color="Maroon" title="c4">x</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">X</font> &amp; <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K11" title="EQREL_1:func.11">EqClass</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c3">S</font> )
 <b>by </b><i><a class="txt" href="eqrel_1.html#E1:66"><i><font color="Green" title="E33">A1</font></i></a>, <a class="txt" href="eqrel_1.html#E4:66"><i><font color="Green" title="E34">A2</font></i></a>, <a class="ref" href="eqrel_1.html#D8" target="_self" title="EQREL_1:def.8">Def8</a></i>;<br/>


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