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<div><span class="kw">theorem </span><a NAME="T11"><span class="comment"><font color="firebrick">:: RCOMP_1:11</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> is  <a href="xxreal_2.html#V5" title="XXREAL_2:attr.5">real-bounded</a>  &amp; <font color="Olive" title="b1">X</font> is  <a href="rcomp_1.html#V2" title="RCOMP_1:attr.2">closed</a>  holds <br/><font color="Olive" title="b1">X</font> is  <a href="rcomp_1.html#V1" title="RCOMP_1:attr.1">compact</a> </div></div>
