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<div class="add">

<b>let </b><font color="Maroon" title="c1">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> ;<br/>

<b>reconsider </b><font color="Maroon" title="c2">e3</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> 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>  ;<br/>
<a NAME="E2:12"/><i><font color="Green" title="E4">A1</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c1">M</font></span>)</span> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c1">M</font></span>)</span> )
 
;<br/>
<i><font color="Green" title="E5">A2</font></i>: <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> = 
the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a>  <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span>,<span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T5" title="RLVECT_1:th.5">RLVECT_1:5</a></i>
<br/>.= 
<a href="binop_2.html#K27" title="BINOP_2:func.27">addcomplex</a>  <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> ,<a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> 
<b>by </b><i><a class="ref" href="complfld.html#T10" title="COMPLFLD:th.10">COMPLFLD:10</a>, <a class="ref" href="complfld.html#D1" title="COMPLFLD:def.1">COMPLFLD:def 1</a></i>
<br/>.= 
1 <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
<b>by </b><i><a class="ref" href="binop_2.html#D3" title="BINOP_2:def.3">BINOP_2:def 3</a>, <a class="ref" href="complex1.html#D7" title="COMPLEX1:def.7">COMPLEX1:def 7</a></i>
;<br/>
<b>reconsider </b><font color="Maroon" title="c3">rr</font> = 1 <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <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/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> = 
the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a>  <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T5" title="RLVECT_1:th.5">RLVECT_1:5</a></i>
<br/>.= 
<a href="binop_2.html#K27" title="BINOP_2:func.27">addcomplex</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span>,1
<b>by </b><i><a class="ref" href="complfld.html#D1" title="COMPLFLD:def.1">COMPLFLD:def 1</a>, <a class="txt" href="matrix_5.html#E3:12"><i><font color="Green" title="E5">A2</font></i></a>, <a class="ref" href="complex1.html#D7" title="COMPLEX1:def.7">COMPLEX1:def 7</a>, <a class="ref" href="complfld.html#T10" title="COMPLFLD:th.10">COMPLFLD:10</a></i>
<br/>.= 
<font color="Maroon" title="c3">rr</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
<b>by </b><i><a class="ref" href="binop_2.html#D3" title="BINOP_2:def.3">BINOP_2:def 3</a>, <a class="ref" href="complex1.html#D7" title="COMPLEX1:def.7">COMPLEX1:def 7</a></i>
<br/>.= 
3

;<br/>
<b>then </b>3 <a href="matrix_5.html#K7" title="MATRIX_5:func.7">*</a> <font color="Maroon" title="c1">M</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">e3</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">M</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#K2" title="MATRIX_5:func.2">Field2COMPLEX</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p3">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c1">M</font></span>)</span></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span>)</span> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p3">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c1">M</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#T13" target="_self" title="MATRIX_5:th.13">Th13</a></i>
<br/>.= 
 <a href="matrix_5.html#K2" title="MATRIX_5:func.2">Field2COMPLEX</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c1">M</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span>)</span> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p3">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c1">M</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#T10" target="_self" title="MATRIX_5:th.10">Th10</a></i>
<br/>.= 
 <a href="matrix_5.html#K2" title="MATRIX_5:func.2">Field2COMPLEX</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c1">M</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <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="c1">M</font></span>)</span></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <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="c1">M</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#T13" target="_self" title="MATRIX_5:th.13">Th13</a></i>
<br/>.= 
 <a href="matrix_5.html#K2" title="MATRIX_5:func.2">Field2COMPLEX</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c1">M</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c1">M</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <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="c1">M</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#T10" target="_self" title="MATRIX_5:th.10">Th10</a></i>
<br/>.= 
 <a href="matrix_5.html#K2" title="MATRIX_5:func.2">Field2COMPLEX</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c1">M</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c1">M</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p3">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c1">M</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#T10" target="_self" title="MATRIX_5:th.10">Th10</a></i>
<br/>.= 
 <a href="matrix_5.html#K2" title="MATRIX_5:func.2">Field2COMPLEX</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c1">M</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p3">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c1">M</font></span>)</span></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</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">M</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_3.html#T5" title="MATRIX_3:th.5">MATRIX_3:5</a>, <a class="txt" href="matrix_5.html#E2:12"><i><font color="Green" title="E4">A1</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E7:12"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="matrix_5.html#K3" title="MATRIX_5:func.3">+</a> <font color="Maroon" title="c1">M</font></span>)</span> <a href="matrix_5.html#K3" title="MATRIX_5:func.3">+</a> <font color="Maroon" title="c1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 <a href="matrix_5.html#K7" title="MATRIX_5:func.7">*</a> <font color="Maroon" title="c1">M</font>
 ;<br/>


</div>
