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<b>let </b><font color="Maroon">A</font> be   <a href="roughs_1.html#NM2">Tolerance_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">Y</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">Z</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">A</font>;<br/>







<b>assume </b><a NAME="E1:93"/>
( <font color="Maroon">X</font> <a href="roughs_1.html#R2" target="_self">c=^</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">Y</font> <a href="roughs_1.html#R2" target="_self">c=^</a> <font color="Maroon">Z</font> )
 ;<br/>

<a NAME="E2:93"/><b>then </b>
(  <a href="roughs_1.html#K4" target="_self">UAp</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="roughs_1.html#K4" target="_self">UAp</a> <font color="Maroon">Y</font> &amp;  <a href="roughs_1.html#K4" target="_self">UAp</a> <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a>  <a href="roughs_1.html#K4" target="_self">UAp</a> <font color="Maroon">Z</font> )
 
<b>by </b><i><a class="ref" href="roughs_1.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E3:93"/><b>then </b>
 <a href="roughs_1.html#K4" target="_self">UAp</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="roughs_1.html#K4" target="_self">UAp</a> <font color="Maroon">Z</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E4:93"/>
<font color="Maroon">X</font> <a href="roughs_1.html#R2" target="_self">c=^</a> <font color="Maroon">Z</font>
 <b>by </b><i><a class="ref" href="roughs_1.html#T6" target="_self">Th6</a></i>;<br/>


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