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<b>let </b><font color="Maroon" title="c1">a</font> be  <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">M</font> being  <a href="matrix_1.html#NM1" title="MATRIX_1:NM.1">Matrix</a> of <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  holds <br/> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="matrix_5.html#K7" title="MATRIX_5:func.7">*</a> <font color="Olive" title="b1">M</font></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="Olive" title="b1">M</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="matrix_5.html#K7" title="MATRIX_5:func.7">*</a> <font color="Olive" title="b1">M</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Olive" title="b1">M</font> )</span><br/><b>let </b><font color="Maroon" title="c2">M</font> be   <a href="matrix_1.html#NM1" title="MATRIX_1:NM.1">Matrix</a> of <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="matrix_5.html#K7" title="MATRIX_5:func.7">*</a> <font color="Maroon" title="c2">M</font></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="c2">M</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="matrix_5.html#K7" title="MATRIX_5:func.7">*</a> <font color="Maroon" title="c2">M</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c2">M</font> )</span><br/>



<a NAME="E1:4"/>
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> 
 
<b>by </b><i><a class="ref" href="xcmplx_0.html#D2" title="XCMPLX_0:def.2">XCMPLX_0:def 2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c3">ea</font> = <font color="Maroon" title="c1">a</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a>  <b>by </b><i><a class="ref" href="complfld.html#D1" title="COMPLFLD:def.1">COMPLFLD:def 1</a></i>;<br/>
<i><font color="Green" title="E5">A1</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">a</font> <a href="matrix_5.html#K7" title="MATRIX_5:func.7">*</a> <font color="Maroon" title="c2">M</font></span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="matrix_5.html#K7" title="MATRIX_5:func.7">*</a> <font color="Maroon" title="c2">M</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#T7" title="MATRIX_5:th.7">MATRIX_5:7</a></i>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <span class="p2">(<span class="default"><a href="matrix_5.html#K2" title="MATRIX_5:func.2">Field2COMPLEX</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">ea</font> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p4">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c2">M</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#D7" title="MATRIX_5:def.7">MATRIX_5:def 7</a></i>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">ea</font> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p2">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c2">M</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#T6" title="MATRIX_5:th.6">MATRIX_5:6</a></i>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c2">M</font></span>)</span>
<b>by </b><i><a class="ref" href="matrix_3.html#D5" title="MATRIX_3:def.5">MATRIX_3:def 5</a></i>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">M</font>
<b>by </b><i><a class="ref" href="matrix_5.html#D1" title="MATRIX_5:def.1">MATRIX_5:def 1</a></i>
;<br/>
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="matrix_5.html#K7" title="MATRIX_5:func.7">*</a> <font color="Maroon" title="c2">M</font></span>)</span> = 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="matrix_5.html#K7" title="MATRIX_5:func.7">*</a> <font color="Maroon" title="c2">M</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#T7" title="MATRIX_5:th.7">MATRIX_5:7</a></i>
<br/>.= 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <span class="p2">(<span class="default"><a href="matrix_5.html#K2" title="MATRIX_5:func.2">Field2COMPLEX</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">ea</font> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p4">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c2">M</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#D7" title="MATRIX_5:def.7">MATRIX_5:def 7</a></i>
<br/>.= 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">ea</font> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p2">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c2">M</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#T6" title="MATRIX_5:th.6">MATRIX_5:6</a></i>
<br/>.= 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c2">M</font></span>)</span>
<b>by </b><i><a class="ref" href="matrix_3.html#D5" title="MATRIX_3:def.5">MATRIX_3:def 5</a></i>
<br/>.= 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c2">M</font>
<b>by </b><i><a class="ref" href="matrix_5.html#D1" title="MATRIX_5:def.1">MATRIX_5:def 1</a></i>
;<br/>
<b>hence </b><a NAME="E5:4"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="matrix_5.html#K7" title="MATRIX_5:func.7">*</a> <font color="Maroon" title="c2">M</font></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="c2">M</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="matrix_5.html#K7" title="MATRIX_5:func.7">*</a> <font color="Maroon" title="c2">M</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c2">M</font> )
 <b>by </b><i><a class="txt" href="#E3:4"><i><font color="Green" title="E5">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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