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<div><span class="kw">theorem </span><a NAME="T54"><span class="comment"><font color="firebrick">:: XXREAL_2:54</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="membered.html#V2" title="MEMBERED:attr.2">ext-real-membered</a>   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st  ex <font color="Olive" title="b2">y</font> being    <a href="xxreal_2.html#M2" title="XXREAL_2:mode.2">LowerBound</a> of <font color="Olive" title="b1">X</font> st <font color="Olive" title="b2">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a>  holds <br/><font color="Olive" title="b1">X</font> is  <a href="xxreal_2.html#V3" title="XXREAL_2:attr.3">bounded_below</a> </div></div>
