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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="matrix_1.html#NM4">Matrix</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:17"/><i><font color="Green">E14</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 ;<br/>

<a NAME="E2:17"/><i><font color="Green">E15</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="matrix_3.html#D2">MATRIX_3:def 2</a></i>;<br/>
<a NAME="E3:17"/><i><font color="Green">E16</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="matrix_3.html#D2">MATRIX_3:def 2</a></i>;<br/>
<a NAME="E4:17"/><i><font color="Green">E17</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="ref" href="matrix_3.html#D2">MATRIX_3:def 2</a></i>;<br/>
<a NAME="E5:17"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is   <a href="matrix_1.html#NM6">Matrix</a> of  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>, <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="matrix_4.html#E1:17"><i><font color="Green">E14</font></i></a>, <a class="ref" href="matrix_1.html#T20">MATRIX_1:20</a></i>;<br/>
<a NAME="E6:17"/><i><font color="Green">E19</font></i>: 
 <a href="matrix_3.html#K2">-</a> <font color="Maroon">c<sub>2</sub></font> is   <a href="matrix_1.html#NM6">Matrix</a> of  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>, <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="matrix_4.html#E1:17"><i><font color="Green">E14</font></i></a>, <a class="txt" href="matrix_4.html#E2:17"><i><font color="Green">E15</font></i></a>, <a class="ref" href="matrix_1.html#T20">MATRIX_1:20</a></i>;<br/>
<a NAME="E7:17"/><i><font color="Green">E20</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="matrix_3.html#K3">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="matrix_3.html#K3">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="matrix_4.html#E2:17"><i><font color="Green">E15</font></i></a>, <a class="ref" href="matrix_3.html#D3">MATRIX_3:def 3</a></i>;<br/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_4.html#K1" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="matrix_4.html#K1" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_4.html#K1" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="matrix_3.html#K3">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="matrix_4.html#K1" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_3.html#K3">+</a> <span class="p2">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="matrix_4.html#E1:17"><i><font color="Green">E14</font></i></a>, <a class="txt" href="matrix_4.html#E2:17"><i><font color="Green">E15</font></i></a>, <a class="ref" href="matrix_3.html#T4">MATRIX_3:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="matrix_3.html#K3">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="matrix_3.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="matrix_3.html#K3">+</a> <span class="p2">(<span class="default"><a href="matrix_3.html#K2">-</a> <span class="p3">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="matrix_4.html#E1:17"><i><font color="Green">E14</font></i></a>, <a class="txt" href="matrix_4.html#E3:17"><i><font color="Green">E16</font></i></a>, <a class="ref" href="matrix_4.html#T12" target="_self">Th12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="matrix_3.html#K3">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="matrix_3.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="matrix_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="matrix_4.html#E1:17"><i><font color="Green">E14</font></i></a>, <a class="ref" href="matrix_4.html#T1" target="_self">Th1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="matrix_3.html#K3">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="matrix_3.html#K3">+</a> <span class="p2">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="matrix_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="matrix_4.html#E1:17"><i><font color="Green">E14</font></i></a>, <a class="txt" href="matrix_4.html#E4:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="matrix_4.html#E7:17"><i><font color="Green">E20</font></i></a>, <a class="ref" href="matrix_3.html#T5">MATRIX_3:5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="matrix_3.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_3.html#K3">+</a> <span class="p3">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="matrix_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="matrix_4.html#E1:17"><i><font color="Green">E14</font></i></a>, <a class="txt" href="matrix_4.html#E2:17"><i><font color="Green">E15</font></i></a>, <a class="txt" href="matrix_4.html#E4:17"><i><font color="Green">E17</font></i></a>, <a class="ref" href="matrix_3.html#T5">MATRIX_3:5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="matrix_3.html#K3">+</a> <span class="p2">(<span class="default"><a href="matrix_3.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="matrix_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="matrix_4.html#E5:17"><i><font color="Green">E18</font></i></a>, <a class="ref" href="matrix_3.html#T7">MATRIX_3:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="matrix_3.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="matrix_4.html#E6:17"><i><font color="Green">E19</font></i></a>, <a class="ref" href="matrix_3.html#T6">MATRIX_3:6</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="matrix_3.html#K3">+</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="matrix_4.html#E1:17"><i><font color="Green">E14</font></i></a>, <a class="txt" href="matrix_4.html#E2:17"><i><font color="Green">E15</font></i></a>, <a class="ref" href="matrix_3.html#T4">MATRIX_3:4</a></i>
;<br/>
<b>hence </b><a NAME="E9:17"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_4.html#K1" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="matrix_4.html#K1" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_4.html#K1" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="matrix_4.html#K1" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>


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