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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E24">Th23</font></span>: <a NAME="T23"><span class="comment"><font color="firebrick">:: LOPBAN_3:23</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b2">seq</font> being   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Olive" title="b1">X</font> holds <br/> (  <a href="series_1.html#K3" title="SERIES_1:func.3">Partial_Sums</a> <span class="p1"><a href="normsp_0.html#K5" title="NORMSP_0:func.5">||.</a><span class="default"><font color="Olive" title="b2">seq</font></span><a href="normsp_0.html#K5" title="NORMSP_0:func.5">.||</a></span> is  <a href="seq_2.html#V1" title="SEQ_2:attr.1">bounded_above</a>  iff <font color="Olive" title="b2">seq</font> is  <a href="lopban_3.html#V2" title="LOPBAN_3:attr.2">norm_summable</a>  )</div></div>
