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<b>let </b><font color="Maroon" title="c1">M1</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> <font color="Maroon" title="c1">M1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="matrix_5.html#K7" title="MATRIX_5:func.7">*</a> <font color="Maroon" title="c1">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_5.html#K8" title="MATRIX_5:func.8">0_Cx</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">M1</font></span>)</span>,<span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c1">M1</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:23"/><i><font color="Green" title="E7">A1</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">M1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="matrix_5.html#K7" title="MATRIX_5:func.7">*</a> <font color="Maroon" title="c1">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_5.html#K8" title="MATRIX_5:func.8">0_Cx</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">M1</font></span>)</span>,<span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c1">M1</font></span>)</span></span><br/>

<b>reconsider </b><font color="Maroon" title="c2">ea</font> =  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  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/>
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="matrix_5.html#K7" title="MATRIX_5:func.7">*</a> <font color="Maroon" title="c1">M1</font> = 
 <a href="matrix_5.html#K2" title="MATRIX_5:func.2">Field2COMPLEX</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">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="c1">M1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#D7" target="_self" title="MATRIX_5:def.7">Def7</a></i>
<br/>.= 
 <a href="matrix_5.html#K8" title="MATRIX_5:func.8">0_Cx</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">M1</font></span>)</span>,<span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c1">M1</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:23"><i><font color="Green" title="E7">A1</font></i></a>, <a class="ref" href="matrix_5.html#T40" target="_self" title="MATRIX_5:th.40">Th40</a>, <a class="ref" href="complfld.html#T9" title="COMPLFLD:th.9">COMPLFLD:9</a></i>
;<br/>
<b>hence </b><a NAME="E4:23"/>
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="matrix_5.html#K7" title="MATRIX_5:func.7">*</a> <font color="Maroon" title="c1">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_5.html#K8" title="MATRIX_5:func.8">0_Cx</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">M1</font></span>)</span>,<span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c1">M1</font></span>)</span>
 ; <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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