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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E15">Th10</font></span>: <a NAME="T11"><span class="comment"><font color="firebrick">:: COUSIN2:11</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="membered.html#V3" title="MEMBERED:attr.3">real-membered</a>   <a href="xxreal_2.html#V3" title="XXREAL_2:attr.3">bounded_below</a>   <a href="xxreal_2.html#V4" title="XXREAL_2:attr.4">bounded_above</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st  <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#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_4.html#K3" title="SEQ_4:func.3">lower_bound</a> <font color="Olive" title="b1">X</font> holds <br/> ex <font color="Olive" title="b2">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> st <font color="Olive" title="b1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="seq_4.html#K1" title="SEQ_4:func.1">{</a><span class="default"><font color="Olive" title="b2">r</font></span><a href="seq_4.html#K1" title="SEQ_4:func.1">}</a></span></div></div>
