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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E9">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: RCOMP_1:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <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>  st <font color="Olive" title="b1">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="b1">X</font> is  <a href="rcomp_1.html#V2" title="RCOMP_1:attr.2">closed</a>  &amp; <font color="Olive" title="b1">X</font> is  <a href="xxreal_2.html#V4" title="XXREAL_2:attr.4">bounded_above</a>  holds <br/> <a href="seq_4.html#K2" title="SEQ_4:func.2">upper_bound</a> <font color="Olive" title="b1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">X</font></div></div>
