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<b>let </b><font color="Maroon">A</font> be   <a href="roughs_1.html#NM1">Approximation_Space</a>;<br/><b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>assume </b><a NAME="E1:62"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="roughs_1.html#K4" target="_self">UAp</a> <font color="Maroon">X</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">A</font> )
 ;<br/>

<a NAME="E2:62"/><b>then </b><i><font color="Green">E27</font></i>: 
 <a href="eqrel_1.html#K7">Class</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">A</font>,<font color="Maroon">x</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">X</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:62"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">x</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">A</font> &amp; <font color="Maroon">y</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">A</font> )
 
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E4:62"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">x</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">A</font>
 
<b>by </b><i>, <a class="ref" href="eqrel_1.html#T12">EQREL_1:12</a></i>;<br/>
<a NAME="E5:62"/><b>then </b>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K7">Class</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">A</font>,<font color="Maroon">x</font>
 
<b>by </b><i><a class="ref" href="eqrel_1.html#T27">EQREL_1:27</a></i>;<br/>
<a NAME="E6:62"/><b>then </b>
 <a href="eqrel_1.html#K7">Class</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">A</font>,<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">A</font>,<font color="Maroon">y</font>
 
<b>by </b><i>, <a class="ref" href="eqrel_1.html#T31">EQREL_1:31</a></i>;<br/>
<b>hence </b><a NAME="E7:62"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="roughs_1.html#K4" target="_self">UAp</a> <font color="Maroon">X</font>
 <b>by </b><i>, <a class="txt" href="roughs_1.html#E4"><i><font color="Green">Lemma32</font></i></a></i>;<br/>


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