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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E17">Th15</font></span>: <a NAME="T18"><span class="comment"><font color="firebrick">:: CHAIN_1:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">Gi</font> being   non  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a><br/>  for <font color="Olive" title="b2">xi</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b2">xi</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">Gi</font> holds <br/> ex <font color="Olive" title="b3">ri</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">xi</font>,<font color="Olive" title="b3">ri</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is    <a href="chain_1.html#M2" title="CHAIN_1:mode.2">Gap</a> of <font color="Olive" title="b1">Gi</font></div></div>
