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<div><span class="kw">theorem </span><a NAME="T24"><span class="comment"><font color="firebrick">:: BHSP_4:24</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="rsspace2.html#NM1" title="RSSPACE2:NM.1">RealHilbertSpace</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/> ( <font color="Olive" title="b2">seq</font> is  <a href="bhsp_4.html#V1" title="BHSP_4:attr.1">summable</a>  iff  for <font color="Olive" title="b3">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b3">r</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/> ex <font color="Olive" title="b4">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/> for <font color="Olive" title="b5">n</font>, <font color="Olive" title="b6">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b5">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Olive" title="b4">k</font> &amp; <font color="Olive" title="b6">m</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Olive" title="b4">k</font> holds <br/><span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><a href="bhsp_4.html#K4" title="BHSP_4:func.4">Sum</a> (<font color="Olive" title="b2">seq</font>,<font color="Olive" title="b5">n</font>,<font color="Olive" title="b6">m</font>)</span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b3">r</font> )</div></div>
