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<span class="kw">reconsider </span><font color="Maroon" title="c1">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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="complfld.html#D1" title="COMPLFLD:def.1">COMPLFLD:def 1</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c2">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">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="c2">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="c2">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="c2">M1</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E2:39"/><span class="lab"><font color="Green" title="E7">A1</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="c2">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="c2">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="c2">M1</font></span>)</span></span><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="c2">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="c1">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">M1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_5.html#D7" target="_self" title="MATRIX_5:def.7">Def7</a></span>
<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="c2">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="c2">M1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:39"><span class="lab"><font color="Green" title="E7">A1</font></span></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></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:39"/>
<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="c2">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="c2">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="c2">M1</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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