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<div><span class="kw">theorem </span><a NAME="T43"><span class="comment"><font color="firebrick">:: BHSP_3:43</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</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>  st <font color="Olive" title="b1">X</font> is  <a href="bhsp_3.html#V3" title="BHSP_3:attr.3">complete</a>  &amp; <font color="Olive" title="b2">seq</font> is  <a href="bhsp_3.html#V1" title="BHSP_3:attr.1">Cauchy</a>  holds <br/><font color="Olive" title="b2">seq</font> is  <a href="bhsp_3.html#V2" title="BHSP_3:attr.2">bounded</a> </div></div>
