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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="E1:94"/>
( <font color="Maroon">X</font> <a href="roughs_1.html#R3" target="_self">_c=^</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">Y</font> <a href="roughs_1.html#R3" target="_self">_c=^</a> <font color="Maroon">Z</font> )
 ;<br/>

<a NAME="E2:94"/><b>then </b>
( <font color="Maroon">X</font> <a href="roughs_1.html#R1" target="_self">_c=</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">Y</font> <a href="roughs_1.html#R1" target="_self">_c=</a> <font color="Maroon">Z</font> &amp; <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> )
 
<b>by </b><i><a class="txt" href="roughs_1.html#E10"><i><font color="Green">Lemma45</font></i></a></i>;<br/>
<a NAME="E3:94"/><b>then </b>
( <font color="Maroon">X</font> <a href="roughs_1.html#R1" target="_self">_c=</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">X</font> <a href="roughs_1.html#R2" target="_self">c=^</a> <font color="Maroon">Z</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:94"/>
<font color="Maroon">X</font> <a href="roughs_1.html#R3" target="_self">_c=^</a> <font color="Maroon">Z</font>
 <b>by </b><i><a class="txt" href="roughs_1.html#E10"><i><font color="Green">Lemma45</font></i></a></i>;<br/>


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