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<div><span class="kw">theorem </span><a NAME="T39"><span class="comment"><font color="firebrick">:: ROUGHIF1:39</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">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b3">x</font>, <font color="Olive" title="b4">y</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">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="roughs_5.html#K6" title="ROUGHS_5:func.6">f_1</a> <font color="Olive" title="b1">R</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">x</font> &amp; <span class="p1">(<span class="default"><a href="roughs_5.html#K2" title="ROUGHS_5:func.2">UncertaintyMap</a> <font color="Olive" title="b1">R</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">y</font> holds <br/> <a href="roughif1.html#K1" title="ROUGHIF1:func.1">kappa</a> (<font color="Olive" title="b4">y</font>,<font color="Olive" title="b3">x</font>) <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a> </div></div>
