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<div><span class="kw">theorem </span><a NAME="T9"><span class="comment"><font color="firebrick">:: INTEGRA2:9</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b2">X</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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>  st <font color="Olive" title="b2">X</font> is  <a href="xxreal_2.html#V4" title="XXREAL_2:attr.4">bounded_above</a>  &amp;  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">r</font> holds <br/><font color="Olive" title="b1">r</font> <a href="integra2.html#K1" title="INTEGRA2:func.1">**</a> <font color="Olive" title="b2">X</font> is  <a href="xxreal_2.html#V4" title="XXREAL_2:attr.4">bounded_above</a> </div></div>
