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<div><span class="kw">theorem </span><a NAME="T27"><span class="comment"><font color="firebrick">:: ROUGHIF1:27</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">Y</font>, <font color="Olive" title="b3">Z</font>, <font color="Olive" title="b4">W</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">R</font>  st <font color="Olive" title="b3">Z</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b2">Y</font> &amp; <font color="Olive" title="b3">Z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">W</font> holds <br/>(  <a href="roughif1.html#K1" title="ROUGHIF1:func.1">kappa</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">Y</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Olive" title="b3">Z</font></span>)</span>,<font color="Olive" title="b4">W</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="roughif1.html#K1" title="ROUGHIF1:func.1">kappa</a> (<font color="Olive" title="b2">Y</font>,<font color="Olive" title="b4">W</font>) &amp;  <a href="roughif1.html#K1" title="ROUGHIF1:func.1">kappa</a> (<font color="Olive" title="b2">Y</font>,<font color="Olive" title="b4">W</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="roughif1.html#K1" title="ROUGHIF1:func.1">kappa</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">Y</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b3">Z</font></span>)</span>,<font color="Olive" title="b4">W</font>) ) <span class="kw">by</span> <span class="lab"><a class="txt" href="roughif1.html#E42"><span class="lab"><font color="Green" title="E30">Test1AAA</font></span></a>, <a class="txt" href="roughif1.html#E43"><span class="lab"><font color="Green" title="E31">Test2AAA</font></span></a></span>;<br/></div></div>
