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<div><span class="kw">theorem </span><a NAME="T25"><span class="comment"><font color="firebrick">:: ROUGHIF1:25</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>, <font color="Olive" title="b4">Z</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="b2">X</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b2">X</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b3">Y</font> holds <br/>(  <a href="roughif1.html#K1" title="ROUGHIF1:func.1">kappa</a> (<font color="Olive" title="b2">X</font>,<span class="p1">(<span class="default"><font color="Olive" title="b4">Z</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Olive" title="b3">Y</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="roughif1.html#K1" title="ROUGHIF1:func.1">kappa</a> (<font color="Olive" title="b2">X</font>,<span class="p1">(<span class="default"><font color="Olive" title="b4">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b3">Y</font></span>)</span>) &amp;  <a href="roughif1.html#K1" title="ROUGHIF1:func.1">kappa</a> (<font color="Olive" title="b2">X</font>,<span class="p1">(<span class="default"><font color="Olive" title="b4">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b3">Y</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="roughif1.html#K1" title="ROUGHIF1:func.1">kappa</a> (<font color="Olive" title="b2">X</font>,<font color="Olive" title="b4">Z</font>) )</div></div>
