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<div><span class="kw">theorem </span><a NAME="T30"><span class="comment"><font color="firebrick">:: ROUGHIF1:30</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>  <a href="roughs_1.html#NM1" title="ROUGHS_1:NM.1">Approximation_Space</a><br/>  for <font color="Olive" title="b2">X</font>, <font color="Olive" title="b3">Y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">R</font> holds <br/> (  <a href="roughif1.html#K1" title="ROUGHIF1:func.1">kappa</a> (<font color="Olive" title="b2">X</font>,<font color="Olive" title="b3">Y</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="roughif1.html#K3" title="ROUGHIF1:func.3">kappa_1</a> (<font color="Olive" title="b2">X</font>,<font color="Olive" title="b3">Y</font>) &amp;  <a href="roughif1.html#K3" title="ROUGHIF1:func.3">kappa_1</a> (<font color="Olive" title="b2">X</font>,<font color="Olive" title="b3">Y</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="roughif1.html#K4" title="ROUGHIF1:func.4">kappa_2</a> (<font color="Olive" title="b2">X</font>,<font color="Olive" title="b3">Y</font>) )</div></div>
