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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E14">Th11</font></span>: <a NAME="T13"><span class="comment"><font color="firebrick">:: CHAIN_1:13</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>  ex <font color="Olive" title="b2">li</font>, <font color="Olive" title="b3">ri</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> st <br/>( <font color="Olive" title="b2">li</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">Gi</font> &amp; <font color="Olive" title="b3">ri</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">Gi</font> &amp; <font color="Olive" title="b2">li</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b3">ri</font> &amp; (  for <font color="Olive" title="b4">xi</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b4">xi</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">Gi</font> &amp; <font color="Olive" title="b2">li</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b4">xi</font> holds <br/> not <font color="Olive" title="b4">xi</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b3">ri</font> ) )</div></div>
