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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="matrix_1.html#NM5">Matrix</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>









<b>assume </b><a NAME="E1:69"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="matrix_6.html#V1" target="_self">Reversible</a> &amp; <font color="Maroon">c<sub>4</sub></font> is <a href="matrix_6.html#V1" target="_self">Reversible</a> &amp; <font color="Maroon">c<sub>5</sub></font> is <a href="matrix_6.html#V1" target="_self">Reversible</a> )
 ;<br/>

<b>set </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span></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#K5" target="_self">~</a> </span>)</span>;<br/>
<a NAME="E2:69"/><i><font color="Green">E26</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>1</sub></font> &amp;  <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</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>1</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#T25">MATRIX_1:25</a></i>;<br/>
<a NAME="E3:69"/><i><font color="Green">E27</font></i>: 
(  <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#K4" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</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#K4" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#T25">MATRIX_1:25</a></i>;<br/>
<a NAME="E4:69"/><i><font color="Green">E28</font></i>: 
(  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#T25">MATRIX_1:25</a></i>;<br/>
<a NAME="E5:69"/><i><font color="Green">E29</font></i>: 
(  <a href="matrix_1.html#K1">width</a> <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#K4" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <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#K4" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#T25">MATRIX_1:25</a></i>;<br/>
<a NAME="E6:69"/><i><font color="Green">E30</font></i>: 
(  <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>1</sub></font> &amp;  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</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>1</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#T25">MATRIX_1:25</a></i>;<br/>
<a NAME="E7:69"/><i><font color="Green">E31</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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#K5" target="_self">~</a> </span>)</span> is   <a href="matrix_1.html#NM4">Matrix</a> of <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"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <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></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <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></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#T25">MATRIX_1:25</a></i>;<br/>
<a NAME="E8:69"/><i><font color="Green">E32</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</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>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> is   <a href="matrix_1.html#NM4">Matrix</a> of <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"><font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#T25">MATRIX_1:25</a></i>;<br/>
<a NAME="E9:69"/><i><font color="Green">E33</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span></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#K5" target="_self">~</a> </span>)</span> is   <a href="matrix_1.html#NM4">Matrix</a> of <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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <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></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <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></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#T25">MATRIX_1:25</a></i>;<br/>
<a NAME="E10:69"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="matrix_6.html#K5" target="_self">~</a>  <a href="matrix_6.html#R2" target="_self">is_reverse_of</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a>  <a href="matrix_6.html#R2" target="_self">is_reverse_of</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K5" target="_self">~</a>  <a href="matrix_6.html#R2" target="_self">is_reverse_of</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="matrix_6.html#E1:69"><i><font color="Green">E25</font></i></a>, <a class="ref" href="matrix_6.html#D4" target="_self">Def4</a></i>;<br/>
<i><font color="Green">E35</font></i>: <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#K4" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <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></span>)</span> = 
<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#K4" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="matrix_6.html#E6:69"><i><font color="Green">E30</font></i></a>, <a class="ref" href="matrix_3.html#T35">MATRIX_3:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <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></span>)</span>
<b>by </b><i><a class="txt" href="matrix_6.html#E5:69"><i><font color="Green">E29</font></i></a>, <a class="txt" href="matrix_6.html#E6:69"><i><font color="Green">E30</font></i></a>, <a class="txt" href="matrix_6.html#E7:69"><i><font color="Green">E31</font></i></a>, <a class="ref" href="matrix_3.html#T35">MATRIX_3:35</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#K4" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span></span>)</span></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <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></span>)</span>
<b>by </b><i><a class="txt" href="matrix_6.html#E2:69"><i><font color="Green">E26</font></i></a>, <a class="txt" href="matrix_6.html#E3:69"><i><font color="Green">E27</font></i></a>, <a class="txt" href="matrix_6.html#E6:69"><i><font color="Green">E30</font></i></a>, <a class="ref" href="matrix_3.html#T35">MATRIX_3:35</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#K4" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <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>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <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></span>)</span>
<b>by </b><i><a class="txt" href="matrix_6.html#E10:69"><i><font color="Green">E34</font></i></a>, <a class="ref" href="matrix_6.html#D2" target="_self">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <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></span>)</span>
<b>by </b><i><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#K4" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span></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#K5" target="_self">~</a> </span>)</span>
<b>by </b><i><a class="txt" href="matrix_6.html#E3:69"><i><font color="Green">E27</font></i></a>, <a class="txt" href="matrix_6.html#E6:69"><i><font color="Green">E30</font></i></a>, <a class="ref" href="matrix_3.html#T35">MATRIX_3:35</a></i>
<br/>.= 
<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"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span></span>)</span></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#K5" target="_self">~</a> </span>)</span>
<b>by </b><i><a class="txt" href="matrix_6.html#E2:69"><i><font color="Green">E26</font></i></a>, <a class="txt" href="matrix_6.html#E6:69"><i><font color="Green">E30</font></i></a>, <a class="ref" href="matrix_3.html#T35">MATRIX_3:35</a></i>
<br/>.= 
<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>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></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#K5" target="_self">~</a> </span>)</span>
<b>by </b><i><a class="txt" href="matrix_6.html#E10:69"><i><font color="Green">E34</font></i></a>, <a class="ref" href="matrix_6.html#D2" target="_self">Def2</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <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#K5" target="_self">~</a> </span>)</span>
<b>by </b><i><a class="ref" href="matrix_3.html#T21">MATRIX_3:21</a></i>
<br/>.= 
 <a href="matrix_1.html#K12">1.</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_6.html#E10:69"><i><font color="Green">E34</font></i></a>, <a class="ref" href="matrix_6.html#D2" target="_self">Def2</a></i>
;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <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></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <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#K4" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <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></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"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="matrix_6.html#E2:69"><i><font color="Green">E26</font></i></a>, <a class="ref" href="matrix_3.html#T35">MATRIX_3:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span></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"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="matrix_6.html#E2:69"><i><font color="Green">E26</font></i></a>, <a class="txt" href="matrix_6.html#E4:69"><i><font color="Green">E28</font></i></a>, <a class="txt" href="matrix_6.html#E9:69"><i><font color="Green">E33</font></i></a>, <a class="ref" href="matrix_3.html#T35">MATRIX_3:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><span class="p3">(<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></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="matrix_6.html#E8:69"><i><font color="Green">E32</font></i></a>, <a class="txt" href="matrix_6.html#E6:69"><i><font color="Green">E30</font></i></a>, <a class="txt" href="matrix_6.html#E2:69"><i><font color="Green">E26</font></i></a>, <a class="ref" href="matrix_3.html#T35">MATRIX_3:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span></span>)</span> <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>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="matrix_6.html#E10:69"><i><font color="Green">E34</font></i></a>, <a class="ref" href="matrix_6.html#D2" target="_self">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="matrix_6.html#E2:69"><i><font color="Green">E26</font></i></a>, <a class="txt" href="matrix_6.html#E8:69"><i><font color="Green">E32</font></i></a>, <a class="ref" href="matrix_3.html#T35">MATRIX_3:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</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>4</sub></font></span>)</span></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="matrix_6.html#E2:69"><i><font color="Green">E26</font></i></a>, <a class="txt" href="matrix_6.html#E6:69"><i><font color="Green">E30</font></i></a>, <a class="ref" href="matrix_3.html#T35">MATRIX_3:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <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>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="matrix_6.html#E10:69"><i><font color="Green">E34</font></i></a>, <a class="ref" href="matrix_6.html#D2" target="_self">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</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>5</sub></font>
<b>by </b><i><a class="ref" href="matrix_3.html#T21">MATRIX_3:21</a></i>
<br/>.= 
 <a href="matrix_1.html#K12">1.</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_6.html#E10:69"><i><font color="Green">E34</font></i></a>, <a class="ref" href="matrix_6.html#D2" target="_self">Def2</a></i>
;<br/>
<a NAME="E13:69"/><b>then </b><i><font color="Green">E36</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span></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#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#R2" target="_self">is_reverse_of</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="matrix_6.html#E11:69"><i><font color="Green">E35</font></i></a>, <a class="ref" href="matrix_6.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E14:69"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font> is <a href="matrix_6.html#V1" target="_self">Reversible</a>
 
<b>by </b><i><a class="ref" href="matrix_6.html#D3" target="_self">Def3</a></i>;<br/>
<b>hence </b><a NAME="E15:69"/>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font> is <a href="matrix_6.html#V1" target="_self">Reversible</a> &amp; <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#K4" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="matrix_6.html#K5" target="_self">~</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K5" target="_self">~</a> </span>)</span></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#K5" target="_self">~</a> </span>)</span> )
 <b>by </b><i><a class="ref" href="matrix_6.html#D4" target="_self">Def4</a>, <a class="txt" href="matrix_6.html#E13:69"><i><font color="Green">E36</font></i></a></i>;<br/>


</div>
