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<b>let </b><font color="Maroon" title="c1">M1</font>, <font color="Maroon" title="c2">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> ; <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="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">M2</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c1">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="c2">M2</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <font color="Maroon" title="c2">M2</font></span>)</span> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">M2</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:16"/><i><font color="Green" title="E14">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="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">M2</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c1">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="c2">M2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <font color="Maroon" title="c2">M2</font></span>)</span> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">M2</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span></span><br/>

<a NAME="E2:16"/><i><font color="Green" title="E15">A2</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <font color="Maroon" title="c2">M2</font></span>)</span> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <font color="Maroon" title="c2">M2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="matrixc1.html#D1" target="_self" title="MATRIXC1:def.1">Def1</a></i>;<br/>
<a NAME="E3:16"/><i><font color="Green" title="E16">A3</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">M1</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </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="c1">M1</font>
 
<b>by </b><i><a class="ref" href="matrixc1.html#D1" target="_self" title="MATRIXC1:def.1">Def1</a></i>;<br/>
<a NAME="E4:16"/><i><font color="Green" title="E17">A4</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="c2">M2</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </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">M2</font>
 
<b>by </b><i><a class="ref" href="matrixc1.html#D1" target="_self" title="MATRIXC1:def.1">Def1</a></i>;<br/>
<a NAME="E5:16"/><i><font color="Green" title="E18">A5</font></i>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </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="c1">M1</font>
 
<b>by </b><i><a class="ref" href="matrixc1.html#D1" target="_self" title="MATRIXC1:def.1">Def1</a></i>;<br/>
<a NAME="E6:16"/><i><font color="Green" title="E19">A6</font></i>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">M2</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </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">M2</font>
 
<b>by </b><i><a class="ref" href="matrixc1.html#D1" target="_self" title="MATRIXC1:def.1">Def1</a></i>;<br/>
<a NAME="E7:16"/><i><font color="Green" title="E20">A7</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">M1</font> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <font color="Maroon" title="c2">M2</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="c1">M1</font>
 
<b>by </b><i><a class="ref" href="matrixc1.html#T13" target="_self" title="MATRIXC1:th.13">Th13</a></i>;<br/>
<a NAME="E8:16"/><i><font color="Green" title="E21">A8</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">M2</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="matrixc1.html#T13" target="_self" title="MATRIXC1:th.13">Th13</a></i>;<br/>
<a NAME="E9:16"/><i><font color="Green" title="E22">A9</font></i>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <font color="Maroon" title="c2">M2</font></span>)</span> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <font color="Maroon" title="c2">M2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="matrixc1.html#D1" target="_self" title="MATRIXC1:def.1">Def1</a></i>;<br/>
<a NAME="E10:16"/><i><font color="Green" title="E23">A10</font></i>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <font color="Maroon" title="c2">M2</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="c1">M1</font>
 
<b>by </b><i><a class="ref" href="matrixc1.html#T13" target="_self" title="MATRIXC1:th.13">Th13</a></i>;<br/>
<a NAME="E11:16"/><i><font color="Green" title="E24">A11</font></i>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">M2</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="matrixc1.html#T13" target="_self" title="MATRIXC1:th.13">Th13</a></i>;<br/>
<a NAME="E12:16"/><i><font color="Green" title="E25">A12</font></i>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </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="c1">M1</font>
 
<b>by </b><i><a class="ref" href="matrixc1.html#D1" target="_self" title="MATRIXC1:def.1">Def1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">i</font>, <font color="Maroon" title="c4">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">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"><span class="p2">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <font color="Maroon" title="c2">M2</font></span>)</span> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <font color="Maroon" title="c2">M2</font></span>)</span> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">M2</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">j</font> )</span><br/><b>assume </b><a NAME="E1:16_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">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"><span class="p2">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <font color="Maroon" title="c2">M2</font></span>)</span> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <font color="Maroon" title="c2">M2</font></span>)</span> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">M2</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">j</font></span><br/><a NAME="E2:16_1"/><b>then </b><i><font color="Green" title="E26">A13</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">i</font> &amp; <font color="Maroon" title="c3">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <font color="Maroon" title="c2">M2</font></span>)</span> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">j</font> &amp; <font color="Maroon" title="c4">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <font color="Maroon" title="c2">M2</font></span>)</span> )
 <b>by </b><i><a class="txt" href="matrixc1.html#E2:16"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="matrixc1.html#E9:16"><i><font color="Green" title="E22">A9</font></i></a>, <a class="ref" href="matrixc1.html#T1" target="_self" title="MATRIXC1:th.1">Th1</a></i>;<br/><a NAME="E3:16_1"/><b>then </b><i><font color="Green" title="E27">A14</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">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"><font color="Maroon" title="c1">M1</font> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <font color="Maroon" title="c2">M2</font></span>)</span>
 <b>by </b><i><a class="ref" href="matrixc1.html#T1" target="_self" title="MATRIXC1:th.1">Th1</a></i>;<br/><a NAME="E4:16_1"/><i><font color="Green" title="E28">A15</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">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="c1">M1</font>
 <b>by </b><i><a class="txt" href="matrixc1.html#E7:16"><i><font color="Green" title="E20">A7</font></i></a>, <a class="txt" href="matrixc1.html#E10:16"><i><font color="Green" title="E23">A10</font></i></a>, <a class="txt" href="matrixc1.html#E2:16_1"><i><font color="Green" title="E26">A13</font></i></a>, <a class="ref" href="matrixc1.html#T1" target="_self" title="MATRIXC1:th.1">Th1</a></i>;<br/><a NAME="E5:16_1"/>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">i</font> &amp; <font color="Maroon" title="c3">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">j</font> &amp; <font color="Maroon" title="c4">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span> )
 <b>by </b><i><a class="txt" href="matrixc1.html#E7:16"><i><font color="Green" title="E20">A7</font></i></a>, <a class="txt" href="matrixc1.html#E10:16"><i><font color="Green" title="E23">A10</font></i></a>, <a class="txt" href="matrixc1.html#E2:16_1"><i><font color="Green" title="E26">A13</font></i></a>, <a class="ref" href="matrixc1.html#D1" target="_self" title="MATRIXC1:def.1">Def1</a></i>;<br/><a NAME="E6:16_1"/><b>then </b><i><font color="Green" title="E29">A16</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">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"><font color="Maroon" title="c1">M1</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span>
 <b>by </b><i><a class="ref" href="matrixc1.html#T1" target="_self" title="MATRIXC1:th.1">Th1</a></i>;<br/><a NAME="E7:16_1"/><i><font color="Green" title="E30">A17</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">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="c2">M2</font>
 <b>by </b><i><a class="txt" href="matrixc1.html#E1:16"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="matrixc1.html#E7:16"><i><font color="Green" title="E20">A7</font></i></a>, <a class="txt" href="matrixc1.html#E10:16"><i><font color="Green" title="E23">A10</font></i></a>, <a class="txt" href="matrixc1.html#E2:16_1"><i><font color="Green" title="E26">A13</font></i></a>, <a class="ref" href="matrixc1.html#T1" target="_self" title="MATRIXC1:th.1">Th1</a></i>;<br/><a NAME="E8:16_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <font color="Maroon" title="c2">M2</font></span>)</span> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <font color="Maroon" title="c2">M2</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">j</font></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a> 
 <b>by </b><i><a class="txt" href="matrixc1.html#E3:16_1"><i><font color="Green" title="E27">A14</font></i></a>, <a class="ref" href="matrixc1.html#D1" target="_self" title="MATRIXC1:def.1">Def1</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <font color="Maroon" title="c2">M2</font></span>)</span> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">j</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">j</font></span>)</span> <a href="binop_2.html#K4" title="BINOP_2:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">M2</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">j</font></span>)</span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a> 
<b>by </b><i><a class="txt" href="matrixc1.html#E1:16"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="matrixc1.html#E4:16_1"><i><font color="Green" title="E28">A15</font></i></a>, <a class="ref" href="matrixc1.html#T14" target="_self" title="MATRIXC1:th.14">Th14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">j</font></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a> </span>)</span> <a href="binop_2.html#K4" title="BINOP_2:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">M2</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">j</font></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a> </span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T120" title="COMPLEX1:th.120">COMPLEX1:120</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">j</font></span>)</span> <a href="binop_2.html#K4" title="BINOP_2:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">M2</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">j</font></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a> </span>)</span>
<b>by </b><i><a class="txt" href="matrixc1.html#E4:16_1"><i><font color="Green" title="E28">A15</font></i></a>, <a class="ref" href="matrixc1.html#D1" target="_self" title="MATRIXC1:def.1">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">j</font></span>)</span> <a href="binop_2.html#K4" title="BINOP_2:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">M2</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">j</font></span>)</span>
<b>by </b><i><a class="txt" href="matrixc1.html#E7:16_1"><i><font color="Green" title="E30">A17</font></i></a>, <a class="ref" href="matrixc1.html#D1" target="_self" title="MATRIXC1:def.1">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">M2</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">j</font>
<b>by </b><i><a class="txt" href="matrixc1.html#E1:16"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="matrixc1.html#E3:16"><i><font color="Green" title="E16">A3</font></i></a>, <a class="txt" href="matrixc1.html#E4:16"><i><font color="Green" title="E17">A4</font></i></a>, <a class="txt" href="matrixc1.html#E5:16"><i><font color="Green" title="E18">A5</font></i></a>, <a class="txt" href="matrixc1.html#E6:16"><i><font color="Green" title="E19">A6</font></i></a>, <a class="txt" href="matrixc1.html#E6:16_1"><i><font color="Green" title="E29">A16</font></i></a>, <a class="ref" href="matrixc1.html#T14" target="_self" title="MATRIXC1:th.14">Th14</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E14:16"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <font color="Maroon" title="c2">M2</font></span>)</span> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M1</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span> <a href="matrix_5.html#K5" title="MATRIX_5:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">M2</font> <a href="matrixc1.html#K1" title="MATRIXC1:func.1">*'</a> </span>)</span>
 <b>by </b><i><a class="txt" href="matrixc1.html#E2:16"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="matrixc1.html#E3:16"><i><font color="Green" title="E16">A3</font></i></a>, <a class="txt" href="matrixc1.html#E7:16"><i><font color="Green" title="E20">A7</font></i></a>, <a class="txt" href="matrixc1.html#E8:16"><i><font color="Green" title="E21">A8</font></i></a>, <a class="txt" href="matrixc1.html#E9:16"><i><font color="Green" title="E22">A9</font></i></a>, <a class="txt" href="matrixc1.html#E10:16"><i><font color="Green" title="E23">A10</font></i></a>, <a class="txt" href="matrixc1.html#E11:16"><i><font color="Green" title="E24">A11</font></i></a>, <a class="txt" href="matrixc1.html#E12:16"><i><font color="Green" title="E25">A12</font></i></a>, <a class="ref" href="matrix_1.html#T21" title="MATRIX_1:th.21">MATRIX_1:21</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
