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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">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="E1:46"/><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="E2:46"/><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="E3:46"/>
( <font color="Maroon">c</font> <a href="complsp1.html#K14" target="_self">*</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="complsp1.html#K1" target="_self">multcomplex</a> </span>)</span> <a href="finseqop.html#K5">*</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"><font color="Maroon">c</font> <a href="complsp1.html#K14" target="_self">*</a> <font color="Maroon">z</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="complsp1.html#E23"><i><font color="Green">Lemma43</font></i></a>, </i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="complsp1.html#K14" target="_self">*</a> <font color="Maroon">z</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> = 
<span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="complsp1.html#K1" target="_self">multcomplex</a> </span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c'</font>
<b>by </b><i><a class="ref" href="complsp1.html#T16" target="_self">Th16</a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>
<br/>.= 
<font color="Maroon">c</font> <a href="binop_2.html#K5">*</a> <font color="Maroon">c'</font>
<b>by </b><i/>
;<br/><br/>


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