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<b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">c</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/><b>let </b><font color="Maroon">z</font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="complsp1.html#K8" target="_self">COMPLEX</a> <font color="Maroon">n</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:54"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font>
 <b>and </b><br/><a NAME="E2:54"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 ;<br/>

<a NAME="E3:54"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="complsp1.html#K15" target="_self">abs</a> <font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>;<br/>
<a NAME="E4:54"/><b>then </b>
( <a href="complsp1.html#K2" target="_self">abscomplex</a>  <a href="finseqop.html#K5">*</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="complsp1.html#K15" target="_self">abs</a> <font color="Maroon">z</font> &amp; <font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="complsp1.html#K15" target="_self">abs</a> <font color="Maroon">z</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="complsp1.html#T16" target="_self">Th16</a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="complsp1.html#K15" target="_self">abs</a> <font color="Maroon">z</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> = 
<a href="complsp1.html#K2" target="_self">abscomplex</a>  <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="ref" href="complsp1.html#T17" target="_self">Th17</a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>
<br/>.= 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">c</font></span><a href="complex1.html#K17">.|</a></span>
<b>by </b><i/>
;<br/><br/>


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