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<b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</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>given </b><font color="Maroon">c<sub>7</sub></font> being   <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><b> such that </b><a NAME="E1:35_1_2"/><i><font color="Green">E7</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> is <a href="matrix_6.html#V1">Reversible</a> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="matrix_6.html#K5">~</a> </span>)</span> <a href="matrix_6.html#K4">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="matrix_6.html#K4">*</a> <font color="Maroon">c<sub>7</sub></font> )
 ;<br/>

<a NAME="E2:35_1_2"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="matrix_6.html#K5">~</a>  <a href="matrix_6.html#R2">is_reverse_of</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="matrix_8.html#E1:35_1_2"><i><font color="Green">E7</font></i></a>, <a class="ref" href="matrix_6.html#D4">MATRIX_6:def 4</a></i>;<br/>
<a NAME="E3:35_1_2"/><i><font color="Green">E9</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</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>6</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>7</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>7</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="E4:35_1_2"/><i><font color="Green">E10</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="matrix_6.html#K5">~</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>7</sub></font> <a href="matrix_6.html#K5">~</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="E5:35_1_2"/><i><font color="Green">E11</font></i>: 
(  <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>7</sub></font> <a href="matrix_6.html#K5">~</a> </span>)</span> <a href="matrix_6.html#K4">*</a> <font color="Maroon">c<sub>6</sub></font></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"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="matrix_6.html#K5">~</a> </span>)</span> <a href="matrix_6.html#K4">*</a> <font color="Maroon">c<sub>6</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/>
<i><font color="Green">E12</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="matrix_6.html#K5">~</a> </span>)</span> <a href="matrix_6.html#K5">~</a> </span>)</span> <a href="matrix_6.html#K4">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="matrix_6.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="matrix_6.html#K5">~</a> </span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="matrix_6.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="matrix_6.html#K5">~</a> </span>)</span> <a href="matrix_6.html#K4">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="matrix_6.html#K4">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="matrix_6.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="matrix_6.html#K5">~</a> </span>)</span>
<b>by </b><i><a class="txt" href="matrix_8.html#E1:35_1_2"><i><font color="Green">E7</font></i></a>, <a class="ref" href="matrix_6.html#T16">MATRIX_6:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="matrix_6.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="matrix_6.html#K5">~</a> </span>)</span> <a href="matrix_6.html#K4">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="matrix_6.html#K4">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="matrix_6.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="matrix_6.html#K5">~</a> </span>)</span>
<b>by </b><i><a class="txt" href="matrix_8.html#E3:35_1_2"><i><font color="Green">E9</font></i></a>, <a class="txt" href="matrix_8.html#E5:35_1_2"><i><font color="Green">E11</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>7</sub></font> <a href="matrix_6.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="matrix_6.html#K5">~</a> </span>)</span></span>)</span> <a href="matrix_6.html#K4">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="matrix_6.html#K4">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="matrix_6.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="matrix_6.html#K5">~</a> </span>)</span>
<b>by </b><i><a class="txt" href="matrix_8.html#E3:35_1_2"><i><font color="Green">E9</font></i></a>, <a class="txt" href="matrix_8.html#E4:35_1_2"><i><font color="Green">E10</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"><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> <a href="matrix_6.html#K4">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="matrix_6.html#K4">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="matrix_6.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="matrix_6.html#K5">~</a> </span>)</span>
<b>by </b><i><a class="txt" href="matrix_8.html#E2:35_1_2"><i><font color="Green">E8</font></i></a>, <a class="ref" href="matrix_6.html#D2">MATRIX_6:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="matrix_6.html#K4">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="matrix_6.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="matrix_6.html#K5">~</a> </span>)</span>
<b>by </b><i><a class="ref" href="matrix_3.html#T20">MATRIX_3:20</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="matrix_6.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="matrix_6.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="matrix_6.html#K5">~</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="matrix_8.html#E3:35_1_2"><i><font color="Green">E9</font></i></a>, <a class="txt" href="matrix_8.html#E4:35_1_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="matrix_3.html#T35">MATRIX_3:35</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="matrix_6.html#K4">*</a> <span class="p1">(<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>
<b>by </b><i><a class="txt" href="matrix_8.html#E2:35_1_2"><i><font color="Green">E8</font></i></a>, <a class="ref" href="matrix_6.html#D2">MATRIX_6:def 2</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="ref" href="matrix_3.html#T21">MATRIX_3:21</a></i>
;<br/>
<b>take </b>
<font color="Maroon">c<sub>7</sub></font> <a href="matrix_6.html#K5">~</a> 
;<br/>

<b>thus </b><a NAME="E7:35_1_2"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="matrix_6.html#K5">~</a>  is <a href="matrix_6.html#V1">Reversible</a> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="matrix_6.html#K5">~</a> </span>)</span> <a href="matrix_6.html#K5">~</a> </span>)</span> <a href="matrix_6.html#K4">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="matrix_6.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="matrix_6.html#K5">~</a> </span>)</span> )
 <b>by </b><i><a class="txt" href="matrix_8.html#E6:35_1_2"><i><font color="Green">E12</font></i></a>, <a class="txt" href="matrix_8.html#E1:35_1_2"><i><font color="Green">E7</font></i></a>, <a class="ref" href="matrix_6.html#T16">MATRIX_6:16</a></i>;<br/>


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