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<b>let </b><font color="Maroon" title="c1">z</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ;<br/>

<a NAME="E1:27"/><i><font color="Green" title="E23">A1</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a> </span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="complsp2.html#D1" target="_self" title="COMPLSP2:def.1">Def1</a></i>;<br/>
<a NAME="E2:27"/><i><font color="Green" title="E24">A2</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">z</font>
 
<b>by </b><i><a class="ref" href="complsp2.html#D1" target="_self" title="COMPLSP2:def.1">Def1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:27_1"/>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">i</font> &amp; <font color="Maroon" title="c2">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a> </span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a> </span>)</span> )
 ;<br/><a NAME="E2:27_1"/><b>then </b><i><font color="Green" title="E25">A3</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">i</font> &amp; <font color="Maroon" title="c2">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a> </span>)</span> )
 <b>by </b><i><a class="ref" href="complsp2.html#D1" target="_self" title="COMPLSP2:def.1">Def1</a></i>;<br/><a NAME="E3:27_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a> </span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a> 
 <b>by </b><i><a class="ref" href="complsp2.html#D1" target="_self" title="COMPLSP2:def.1">Def1</a>, <a class="txt" href="complsp2.html#E2:27"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="complsp2.html#E2:27_1"><i><font color="Green" title="E25">A3</font></i></a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a> </span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a> </span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c2">i</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a> </span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a> 
<b>by </b><i><a class="txt" href="complsp2.html#E2:27_1"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="complsp2.html#D1" target="_self" title="COMPLSP2:def.1">Def1</a></i>
<br/>.= 
<font color="Maroon" title="c1">z</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c2">i</font>

;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:27"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a> </span>)</span> <a href="complsp2.html#K1" title="COMPLSP2:func.1">*'</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">z</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#T18" title="FINSEQ_1:th.18">FINSEQ_1:18</a>, <a class="txt" href="complsp2.html#E2:27"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="complsp2.html#E1:27"><i><font color="Green" title="E23">A1</font></i></a></i>;<br/>


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