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<b>let </b><font color="Maroon">seq</font> be   <a href="comseq_1.html#NM1">Complex_Sequence</a>;<br/><b>let </b><font color="Maroon">seq1</font> be   <a href="comseq_1.html#NM1">Complex_Sequence</a>;<br/>



<b>assume </b><a NAME="E1:47"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">seq</font> is <a href="comseq_1.html#V1" target="_self">non-zero</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><a NAME="E1:47_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">seq</font> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">n</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="complex1.html#K5">0c</a> 
 <b>by </b><i>, </i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">seq1</font> <a href="comseq_1.html#K8" target="_self">/"</a> <font color="Maroon">seq</font></span>)</span> <a href="comseq_1.html#K3" target="_self">(#)</a> <font color="Maroon">seq</font></span>)</span> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">n</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">seq1</font> <a href="comseq_1.html#K3" target="_self">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">seq</font> <a href="comseq_1.html#K7" target="_self">"</a> </span>)</span></span>)</span> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">n</font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">seq1</font> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">n</font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">seq</font> <a href="comseq_1.html#K7" target="_self">"</a> </span>)</span> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">seq1</font> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">n</font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">seq</font> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">n</font></span>)</span> <a href="complex1.html#K12">"</a> </span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">seq1</font> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">n</font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">seq</font> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">n</font></span>)</span> <a href="complex1.html#K12">"</a> </span>)</span> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">seq</font> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">seq1</font> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">n</font></span>)</span> <a href="complex1.html#K9">*</a> <a href="complex1.html#K6">1r</a> 
<b>by </b><i>, <a class="ref" href="complex1.html#D7">COMPLEX1:def 7</a>, <a class="ref" href="xcmplx_0.html#D7">XCMPLX_0:def 7</a></i>
<br/>.= 
<font color="Maroon">seq1</font> <a href="comseq_1.html#K1" target="_self">.</a> <font color="Maroon">n</font>
<b>by </b><i><a class="ref" href="complex1.html#D7">COMPLEX1:def 7</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:47"/>
<span class="p1">(<span class="default"><font color="Maroon">seq1</font> <a href="comseq_1.html#K8" target="_self">/"</a> <font color="Maroon">seq</font></span>)</span> <a href="comseq_1.html#K3" target="_self">(#)</a> <font color="Maroon">seq</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">seq1</font>
 <b>by </b><i/>;<br/>


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