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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E43">Th53</font></span>: <a NAME="T53"><span class="comment"><font color="firebrick">:: COMSEQ_3:53</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>  st <font color="Olive" title="b1">seq</font> is  <a href="comseq_3.html#V1" title="COMSEQ_3:attr.1">summable</a>  holds <br/>(  <a href="comseq_3.html#K7" title="COMSEQ_3:func.7">Re</a> <font color="Olive" title="b1">seq</font> is  <a href="series_1.html#V1" title="SERIES_1:attr.1">summable</a>  &amp;  <a href="comseq_3.html#K8" title="COMSEQ_3:func.8">Im</a> <font color="Olive" title="b1">seq</font> is  <a href="series_1.html#V1" title="SERIES_1:attr.1">summable</a>  &amp;  <a href="comseq_3.html#K11" title="COMSEQ_3:func.11">Sum</a> <font color="Olive" title="b1">seq</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="series_1.html#K4" title="SERIES_1:func.4">Sum</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="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="series_1.html#K4" title="SERIES_1:func.4">Sum</a> <span class="p3">(<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="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a></span>)</span> )</div></div>
