<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E27">Th32</font></span>: <a NAME="T32"><span class="comment"><font color="firebrick">:: COMSEQ_3:32</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">seq</font> being   <a href="comseq_1.html#NM1" title="COMSEQ_1:NM.1">Complex_Sequence</a><br/>  for <font color="Olive" title="b2">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds <br/> ( <span class="p1">(<span class="default"><a href="series_1.html#K3" title="SERIES_1:func.3">Partial_Sums</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K7" title="COMSEQ_3:func.7">Re</a> <font color="Olive" title="b1">seq</font></span>)</span></span>)</span> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> <font color="Olive" title="b2">k</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="comseq_3.html#K7" title="COMSEQ_3:func.7">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comseq_3.html#K10" title="COMSEQ_3:func.10">Partial_Sums</a> <font color="Olive" title="b1">seq</font></span>)</span> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> <font color="Olive" title="b2">k</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="series_1.html#K3" title="SERIES_1:func.3">Partial_Sums</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K8" title="COMSEQ_3:func.8">Im</a> <font color="Olive" title="b1">seq</font></span>)</span></span>)</span> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> <font color="Olive" title="b2">k</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="comseq_3.html#K8" title="COMSEQ_3:func.8">Im</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comseq_3.html#K10" title="COMSEQ_3:func.10">Partial_Sums</a> <font color="Olive" title="b1">seq</font></span>)</span> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> <font color="Olive" title="b2">k</font></span>)</span> )</div></div>
