<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E38">Th32</font></span>: <a NAME="T32"><span class="comment"><font color="firebrick">:: CLOPBAN4:32</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="clopban2.html#NM3" title="CLOPBAN2:NM.3">Complex_Banach_Algebra</a><br/>  for <font color="Olive" title="b2">w</font>, <font color="Olive" title="b3">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b4">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 (  for <font color="Olive" title="b5">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Olive" title="b4">seq</font> <a href="normsp_0.html#K1" title="NORMSP_0:func.1">.</a> <font color="Olive" title="b5">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <span class="p2">(<span class="default"><a href="clopban4.html#K5" title="CLOPBAN4:func.5">Conj</a> (<font color="Olive" title="b5">k</font>,<font color="Olive" title="b3">z</font>,<font color="Olive" title="b2">w</font>)</span>)</span></span>)</span> <a href="normsp_0.html#K1" title="NORMSP_0:func.1">.</a> <font color="Olive" title="b5">k</font> ) holds <br/>( <font color="Olive" title="b4">seq</font> is  <a href="clvect_1.html#V9" title="CLVECT_1:attr.9">convergent</a>  &amp;  <a href="clvect_1.html#K7" title="CLVECT_1:func.7">lim</a> <font color="Olive" title="b4">seq</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b1">X</font> )</div></div>
