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<b>let </b><font color="Maroon">c</font> be  <a href="comseq_2.html#V2">convergent</a> <a href="comseq_1.html#NM1">Complex_Sequence</a>;<br/>

<a NAME="E1:53"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <span class="p1">(<span class="default"><a href="comseq_3.html#K3" target="_self">Re</a> <font color="Maroon">c</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="comseq_1.html#K1">.</a> <font color="Olive">n</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E2:53"/>
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <span class="p1">(<span class="default"><a href="comseq_3.html#K4" target="_self">Im</a> <font color="Maroon">c</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="comseq_1.html#K1">.</a> <font color="Olive">n</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:53"/>
(  <a href="comseq_3.html#K3" target="_self">Re</a> <font color="Maroon">c</font> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="comseq_3.html#K4" target="_self">Im</a> <font color="Maroon">c</font> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K3" target="_self">Re</a> <font color="Maroon">c</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2">lim</a> <font color="Maroon">c</font></span>)</span> &amp;  <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K4" target="_self">Im</a> <font color="Maroon">c</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2">lim</a> <font color="Maroon">c</font></span>)</span> )
 <b>by </b><i><a class="txt" href="comseq_3.html#E1:53"><i><font color="Green">E35</font></i></a>, <a class="txt" href="comseq_3.html#E1"><i><font color="Green">Lemma33</font></i></a></i>;<br/>


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