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<div><span class="kw">theorem </span><a NAME="T20"><span class="comment"><font color="firebrick">:: COMSEQ_3:20</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">z</font> being   <a href="xcmplx_0.html#NM1" title="XCMPLX_0:NM.1">Complex</a> holds <br/> (  <a href="comseq_3.html#K7" title="COMSEQ_3:func.7">Re</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">z</font> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <font color="Olive" title="b1">seq</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Olive" title="b2">z</font></span>)</span> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</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_1.html#K47" title="VALUED_1:func.47">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Olive" title="b2">z</font></span>)</span> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</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> &amp;  <a href="comseq_3.html#K8" title="COMSEQ_3:func.8">Im</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">z</font> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <font color="Olive" title="b1">seq</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Olive" title="b2">z</font></span>)</span> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</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="series_1.html#K1" title="SERIES_1:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Olive" title="b2">z</font></span>)</span> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</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> )</div></div>
