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<b>let </b><font color="Maroon" title="c1">i</font>, <font color="Maroon" title="c2">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>let </b><font color="Maroon" title="c3">M1</font>, <font color="Maroon" title="c4">M2</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>assume </b><a NAME="E1:8"/><i><font color="Green" title="E9">A1</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">M1</font> <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="c4">M2</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c3">M1</font> <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="c4">M2</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <font color="Maroon" title="c3">M1</font> )
 ;<br/>

<i><font color="Green" title="E10">A2</font></i>:  <a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_5.html#K3" title="MATRIX_5:func.3">+</a> <font color="Maroon" title="c4">M2</font></span>)</span> = 
 <a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <span class="p1">(<span class="default"><a href="matrix_5.html#K2" title="MATRIX_5:func.2">Field2COMPLEX</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="c3">M1</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="c4">M2</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#D3" title="MATRIX_5:def.3">MATRIX_5:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c3">M1</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p1">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c4">M2</font></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 NAME="E3:8"/><i><font color="Green" title="E11">A3</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c3">M1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="matrix_5.html#D1" title="MATRIX_5:def.1">MATRIX_5:def 1</a>, <a class="txt" href="matrixc1.html#E1:8"><i><font color="Green" title="E9">A1</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c5">m</font> =  <a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_5.html#K3" title="MATRIX_5:func.3">+</a> <font color="Maroon" title="c4">M2</font></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">m'</font> =  <a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_5.html#K3" title="MATRIX_5:func.3">+</a> <font color="Maroon" title="c4">M2</font></span>)</span> as   <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>  <b>by </b><i><a class="ref" href="complfld.html#D1" title="COMPLFLD:def.1">COMPLFLD:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">m1</font> =  <a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c3">M1</font>, <font color="Maroon" title="c8">m2</font> =  <a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c4">M2</font> as   <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>  <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="E12">A4</font></i>: <font color="Maroon" title="c3">M1</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font> = 
<font color="Maroon" title="c7">m1</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</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/>.= 
<span class="p1">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c3">M1</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>
<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="E13">A5</font></i>: <font color="Maroon" title="c4">M2</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font> = 
<font color="Maroon" title="c8">m2</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</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/>.= 
<span class="p1">(<span class="default"><a href="matrix_5.html#K1" title="MATRIX_5:func.1">COMPLEX2Field</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>
<b>by </b><i><a class="ref" href="complfld.html#D1" title="COMPLFLD:def.1">COMPLFLD:def 1</a></i>
;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_5.html#K3" title="MATRIX_5:func.3">+</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font> = 
<font color="Maroon" title="c6">m'</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</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/>.= 
<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="c3">M1</font> <a href="matrix_5.html#K3" title="MATRIX_5:func.3">+</a> <font color="Maroon" title="c4">M2</font></span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>
<b>by </b><i><a class="ref" href="complfld.html#D1" title="COMPLFLD:def.1">COMPLFLD:def 1</a></i>
<br/>.= 
<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="c3">M1</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</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="c4">M2</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font></span>)</span>
<b>by </b><i><a class="txt" href="matrixc1.html#E3:8"><i><font color="Green" title="E11">A3</font></i></a>, <a class="ref" href="matrix_3.html#D3" title="MATRIX_3:def.3">MATRIX_3:def 3</a>, <a class="txt" href="matrixc1.html#E2:8"><i><font color="Green" title="E10">A2</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E9:8"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_5.html#K3" title="MATRIX_5:func.3">+</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font></span>)</span> <a href="binop_2.html#K3" title="BINOP_2:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font></span>)</span>
 <b>by </b><i><a class="txt" href="matrixc1.html#E6:8"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="matrixc1.html#E7:8"><i><font color="Green" title="E13">A5</font></i></a>, <a class="ref" href="complfld.html#T3" title="COMPLFLD:th.3">COMPLFLD:3</a></i>;<br/>


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