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<div><span class="kw">theorem </span><a NAME="T33"><span class="comment"><font color="firebrick">:: ROUGHIF1:33</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="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="b2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</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="b2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b3">Y</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="roughif1.html#K3" title="ROUGHIF1:func.3">kappa_1</a> (<font color="Olive" title="b2">X</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b3">Y</font></span>)</span>) &amp;  <a href="roughif1.html#K3" title="ROUGHIF1:func.3">kappa_1</a> (<font color="Olive" title="b2">X</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b3">Y</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="roughif1.html#K3" title="ROUGHIF1:func.3">kappa_1</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">X</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Olive" title="b3">Y</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b3">Y</font></span>)</span>) ) <span class="kw">by</span> <span class="lab"><a class="txt" href="roughif1.html#E49"><span class="lab"><font color="Green" title="E34">LemmaKap1</font></span></a>, <a class="txt" href="roughif1.html#E50"><span class="lab"><font color="Green" title="E35">LemmaKap2</font></span></a>, <a class="txt" href="roughif1.html#E51"><span class="lab"><font color="Green" title="E36">LemmaKap3</font></span></a></span>;<br/></div></div>
