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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> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="matrix_1.html#NM5">Matrix</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:19"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12">1.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="matrix_1.html#K5">@</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 ;<br/>

<a NAME="E2:19"/><b>then </b><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K12">1.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="matrix_6.html#T10" target="_self">Th10</a></i>;<br/>
<a NAME="E3:19"/><i><font color="Green">E13</font></i>: 
(  <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</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> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="hidden.html#R1">=</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_1.html#K12">1.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12">1.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#T25">MATRIX_1:25</a></i>;<br/>
<a NAME="E4:19"/><i><font color="Green">E14</font></i>: 
( <span class="p1">(<span class="default"><a href="matrix_1.html#K12">1.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12">1.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K12">1.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp; <span class="p1">(<span class="default"><a href="matrix_1.html#K12">1.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12">1.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12">1.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12">1.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="matrix_3.html#T20">MATRIX_3:20</a></i>;<br/>
<b>then </b><font color="Maroon">c<sub>3</sub></font> <a href="matrix_6.html#K5" target="_self">~</a>  = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K12">1.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="matrix_6.html#E2:19"><i><font color="Green">E12</font></i></a>, <a class="ref" href="matrix_3.html#T21">MATRIX_3:21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12">1.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="matrix_6.html#E3:19"><i><font color="Green">E13</font></i></a>, <a class="ref" href="matrix_3.html#T35">MATRIX_3:35</a></i>
<br/>.= 
 <a href="matrix_1.html#K12">1.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="matrix_6.html#E2:19"><i><font color="Green">E12</font></i></a>, <a class="txt" href="matrix_6.html#E4:19"><i><font color="Green">E14</font></i></a>, <a class="ref" href="matrix_6.html#T8" target="_self">Th8</a></i>
;<br/>
<b>hence </b><a NAME="E6:19"/>
<font color="Maroon">c<sub>3</sub></font> <a href="matrix_6.html#K5" target="_self">~</a>  <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K12">1.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 ;<br/>


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