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<b>let </b><font color="Maroon">Y</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">PA</font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>, <font color="Maroon">PB</font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>;<br/>



<b>assume </b><a NAME="E1:4"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">PA</font> <a href="partit1.html#NR2" target="_self">'&gt;'</a> <font color="Maroon">PB</font> &amp; <font color="Maroon">PB</font> <a href="partit1.html#NR2" target="_self">'&gt;'</a> <font color="Maroon">PA</font> )
 ;<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="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:4"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">PB</font>
 ;<br/>

<b>then consider </b><font color="Maroon">V</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:4"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">V</font> <a href="hidden.html#R2">in</a> <font color="Maroon">PA</font> &amp; <font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V</font> )
 <b>by </b><i>, <a class="ref" href="setfam_1.html#D2">SETFAM_1:def 2</a></i>;<br/>
<b>consider </b><font color="Maroon">W</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:4"/><i><font color="Green">E48</font></i>: 
( <font color="Maroon">W</font> <a href="hidden.html#R2">in</a> <font color="Maroon">PB</font> &amp; <font color="Maroon">V</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">W</font> )
 <b>by </b><i>, , <a class="ref" href="setfam_1.html#D2">SETFAM_1:def 2</a></i>;<br/>
<a NAME="E7:4"/>
<font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">W</font>
 
<b>by </b><i>, , <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E8:4"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W</font>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E9:4"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">PA</font>
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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