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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E15">Th9</font></span>: <a NAME="T11"><span class="comment"><font color="firebrick">:: INTEGRA1:11</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">f</font> being   <a href="valued_0.html#V3" title="VALUED_0:attr.3">real-valued</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">f</font> is  <a href="seq_2.html#V2" title="SEQ_2:attr.2">bounded_below</a>  holds <br/> <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Olive" title="b1">f</font> is  <a href="xxreal_2.html#V3" title="XXREAL_2:attr.3">bounded_below</a> </div></div>
