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<b>let </b><font color="Maroon">K</font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">n</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">M1</font> be   <a href="matrix_1.html#NM5">Matrix</a> of <font color="Maroon">n</font>,<font color="Maroon">K</font>;<br/><b>let </b><font color="Maroon">M2</font> be   <a href="matrix_1.html#NM5">Matrix</a> of <font color="Maroon">n</font>,<font color="Maroon">K</font>;<br/><b>let </b><font color="Maroon">M3</font> be   <a href="matrix_1.html#NM5">Matrix</a> of <font color="Maroon">n</font>,<font color="Maroon">K</font>;<br/><b>let </b><font color="Maroon">M4</font> be   <a href="matrix_1.html#NM5">Matrix</a> of <font color="Maroon">n</font>,<font color="Maroon">K</font>;<br/>











<a NAME="E1:21"/><i><font color="Green">E35</font></i>: 
(  <a href="matrix_1.html#K1">width</a> <font color="Maroon">M1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp;  <a href="matrix_1.html#K1">width</a> <font color="Maroon">M2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp;  <a href="matrix_1.html#K1">width</a> <font color="Maroon">M3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp;  <a href="matrix_1.html#K1">width</a> <font color="Maroon">M4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#T25">MATRIX_1:25</a></i>;<br/>
<b>assume </b><a NAME="E2:21"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">M3</font> <a href="matrix_6.html#R2" target="_self">is_reverse_of</a> <font color="Maroon">M1</font> &amp; <font color="Maroon">M4</font> <a href="matrix_6.html#R2" target="_self">is_reverse_of</a> <font color="Maroon">M2</font> )
 ;<br/>

<a NAME="E3:21"/><i><font color="Green">E38</font></i>: 
(  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><font color="Maroon">M3</font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">M4</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp;  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><font color="Maroon">M2</font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">M1</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#T25">MATRIX_1:25</a></i>;<br/>
<i><font color="Green">E39</font></i>: <span class="p1">(<span class="default"><font color="Maroon">M3</font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">M4</font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">M2</font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">M1</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M3</font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">M4</font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">M2</font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">M1</font>
<b>by </b><i>, , <a class="ref" href="matrix_3.html#T35">MATRIX_3:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">M3</font> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">M4</font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">M2</font></span>)</span></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">M1</font>
<b>by </b><i>, <a class="ref" href="matrix_3.html#T35">MATRIX_3:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">M3</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">K</font>,<font color="Maroon">n</font></span>)</span></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">M1</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">M3</font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">M1</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">K</font>,<font color="Maroon">n</font>
<b>by </b><i>, </i>
;<br/>
<span class="p1">(<span class="default"><font color="Maroon">M2</font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">M1</font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">M3</font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">M4</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M2</font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">M1</font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">M3</font></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">M4</font>
<b>by </b><i>, , <a class="ref" href="matrix_3.html#T35">MATRIX_3:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">M2</font> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">M1</font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">M3</font></span>)</span></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">M4</font>
<b>by </b><i>, <a class="ref" href="matrix_3.html#T35">MATRIX_3:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">M2</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">K</font>,<font color="Maroon">n</font></span>)</span></span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">M4</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">M2</font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">M4</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">K</font>,<font color="Maroon">n</font>
<b>by </b><i>, </i>
;<br/>
<b>hence </b><a NAME="E6:21"/>
<font color="Maroon">M3</font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">M4</font> <a href="matrix_6.html#R2" target="_self">is_reverse_of</a> <font color="Maroon">M2</font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">M1</font>
 <b>by </b><i>, </i>;<br/>


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