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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="matrix_1.html#NM1">Matrix</a> of <a href="numbers.html#K2">COMPLEX</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="xcmplx_0.html#V1">complex</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>assume </b><a NAME="E1:19"/><i><font color="Green">E5</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 ;<br/>

<a NAME="E2:19"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K2">COMPLEX</a> 
 
<b>by </b><i><a class="ref" href="xcmplx_0.html#D2">XCMPLX_0:def 2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <a href="complfld.html#K1">F_Complex</a>  <b>by </b><i><a class="ref" href="complfld.html#D1">COMPLFLD:def 1</a></i>;<br/>
<i><font color="Green">E6</font></i>: <font color="Maroon">c<sub>3</sub></font> <a href="matrix_5.html#K7" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="matrix_5.html#K3" target="_self">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
 <a href="matrix_5.html#K2" target="_self">Field2COMPLEX</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_3.html#K6">*</a> <span class="p2">(<span class="default"><a href="matrix_5.html#K1" target="_self">COMPLEX2Field</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="matrix_5.html#K3" target="_self">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#D7" target="_self">Def7</a></i>
<br/>.= 
 <a href="matrix_5.html#K2" target="_self">Field2COMPLEX</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_3.html#K6">*</a> <span class="p3">(<span class="default"><a href="matrix_5.html#K1" target="_self">COMPLEX2Field</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="matrix_3.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_3.html#K6">*</a> <span class="p3">(<span class="default"><a href="matrix_5.html#K1" target="_self">COMPLEX2Field</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#T36" target="_self">Th36</a>, <a class="txt" href="matrix_5.html#E1:19"><i><font color="Green">E5</font></i></a></i>
;<br/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_5.html#K7" target="_self">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_5.html#K3" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_5.html#K7" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
 <a href="matrix_5.html#K2" target="_self">Field2COMPLEX</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_5.html#K1" target="_self">COMPLEX2Field</a> <span class="p3">(<span class="default"><a href="matrix_5.html#K2" target="_self">Field2COMPLEX</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_3.html#K6">*</a> <span class="p5">(<span class="default"><a href="matrix_5.html#K1" target="_self">COMPLEX2Field</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="matrix_3.html#K3">+</a> <span class="p2">(<span class="default"><a href="matrix_5.html#K1" target="_self">COMPLEX2Field</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_5.html#K7" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#D7" target="_self">Def7</a></i>
<br/>.= 
 <a href="matrix_5.html#K2" target="_self">Field2COMPLEX</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_3.html#K6">*</a> <span class="p3">(<span class="default"><a href="matrix_5.html#K1" target="_self">COMPLEX2Field</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="matrix_3.html#K3">+</a> <span class="p2">(<span class="default"><a href="matrix_5.html#K1" target="_self">COMPLEX2Field</a> <span class="p3">(<span class="default"><a href="matrix_5.html#K2" target="_self">Field2COMPLEX</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_3.html#K6">*</a> <span class="p5">(<span class="default"><a href="matrix_5.html#K1" target="_self">COMPLEX2Field</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#D7" target="_self">Def7</a></i>
<br/>.= 
 <a href="matrix_5.html#K2" target="_self">Field2COMPLEX</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_3.html#K6">*</a> <span class="p3">(<span class="default"><a href="matrix_5.html#K1" target="_self">COMPLEX2Field</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="matrix_3.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_3.html#K6">*</a> <span class="p3">(<span class="default"><a href="matrix_5.html#K1" target="_self">COMPLEX2Field</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>

;<br/>
<b>hence </b><a NAME="E6:19"/>
<font color="Maroon">c<sub>3</sub></font> <a href="matrix_5.html#K7" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="matrix_5.html#K3" target="_self">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_5.html#K7" target="_self">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_5.html#K3" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_5.html#K7" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="matrix_5.html#E4:19"><i><font color="Green">E6</font></i></a></i>;<br/>


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