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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/>



<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:18_1"/>
(  not <font color="Maroon">c<sub>1</sub></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#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> or <font color="Maroon">c<sub>1</sub></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#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1"><b>suppose </b></a><a NAME="E1:18_1_1"/><i><font color="Green">E16</font></i>: 
not <font color="Maroon">c<sub>1</sub></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#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/><div class="add"><a NAME="E2:18_1_1"/><b>then </b><i><font color="Green">E17</font></i>: 
not <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="complsp2.html#T4" target="_self">Th4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="complsp1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="matrix_5.html#K9">.</a> <font color="Maroon">c<sub>1</sub></font> = 
 <a href="binop_2.html#K7">-</a> 0
<b>by </b><i><a class="txt" href="complsp2.html#E1:18_1_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="funct_1.html#D4">FUNCT_1:def 4</a></i>
<br/>.= 
 <a href="binop_2.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="matrix_5.html#K9">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="complsp2.html#E2:18_1_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="funct_1.html#D4">FUNCT_1:def 4</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_2"><b>suppose </b></a><a NAME="E1:18_1_2"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>1</sub></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#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/><div class="add"><b>set </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="matrix_5.html#K9">.</a> <font color="Maroon">c<sub>1</sub></font>;<br/><a NAME="E2:18_1_2"/>
 <a href="complsp1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <a href="binop_2.html#K25">compcomplex</a>  <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="complsp1.html#D9">COMPLSP1:def 9</a></i>;<br/><a NAME="E3:18_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="complsp1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="matrix_5.html#K9">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <a href="binop_2.html#K25">compcomplex</a>  <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="matrix_5.html#K9">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="complsp2.html#E1:18_1_2"><i><font color="Green">E16</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/><b>hence </b><a NAME="E4:18_1_2"/>
<span class="p1">(<span class="default"><a href="complsp1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="matrix_5.html#K9">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="binop_2.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="matrix_5.html#K9">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="binop_2.html#D1">BINOP_2:def 1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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