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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="E1:32"/><i><font color="Green">E20</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="E2:32"/><b>then </b><i><font color="Green">E21</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>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>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="ref" href="matrix_3.html#D2">MATRIX_3:def 2</a></i>;<br/>
<font color="Maroon">c<sub>2</sub></font> <a href="matrix_4.html#K1" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_4.html#K1" target="_self">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
<font color="Maroon">c<sub>2</sub></font> <a href="matrix_3.html#K3">+</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K2">-</a> <span class="p2">(<span class="default"><span class="p3">(<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></span>)</span>
<b>by </b><i><a class="txt" href="matrix_4.html#E1:32"><i><font color="Green">E20</font></i></a>, <a class="txt" href="matrix_4.html#E2:32"><i><font color="Green">E21</font></i></a>, <a class="ref" href="matrix_3.html#T4">MATRIX_3:4</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <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> <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> <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#E1:32"><i><font color="Green">E20</font></i></a>, <a class="txt" href="matrix_4.html#E2:32"><i><font color="Green">E21</font></i></a>, <a class="ref" href="matrix_4.html#T12" target="_self">Th12</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="matrix_3.html#K3">+</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#E1:32"><i><font color="Green">E20</font></i></a>, <a class="ref" href="matrix_4.html#T1" target="_self">Th1</a></i>
;<br/>
<b>hence </b><a NAME="E4:32"/>
<font color="Maroon">c<sub>2</sub></font> <a href="matrix_4.html#K1" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_4.html#K1" target="_self">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="matrix_3.html#K3">+</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>
 ;<br/>


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