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<b>let </b><font color="Maroon">n</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">K</font> be   <a href="vectsp_1.html#NM2">Field</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/>







<a NAME="E1:66"/><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="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> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#T25">MATRIX_1:25</a></i>;<br/>
<b>assume </b><a NAME="E2:66"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Maroon">M1</font> <a href="matrix_6.html#R1" target="_self">commutes_with</a> <font color="Maroon">M2</font> )
 ;<br/>

<b>set </b><font color="Maroon">M3</font> = <font color="Maroon">M1</font> <a href="matrix_1.html#K5">@</a> ;<br/>
<b>set </b><font color="Maroon">M4</font> = <font color="Maroon">M2</font> <a href="matrix_1.html#K5">@</a> ;<br/>
<span class="p1">(<span class="default"><font color="Maroon">M1</font> <a href="matrix_1.html#K5">@</a> </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_1.html#K5">@</a> </span>)</span> = 
<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_1.html#K5">@</a> 
<b>by </b><i>, , <a class="ref" href="matrix_3.html#T24">MATRIX_3:24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">M1</font> <a href="matrix_6.html#K4" target="_self">*</a> <font color="Maroon">M2</font></span>)</span> <a href="matrix_1.html#K5">@</a> 
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">M2</font> <a href="matrix_1.html#K5">@</a> </span>)</span> <a href="matrix_6.html#K4" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">M1</font> <a href="matrix_1.html#K5">@</a> </span>)</span>
<b>by </b><i>, , <a class="ref" href="matrix_3.html#T24">MATRIX_3:24</a></i>
;<br/>
<b>hence </b><a NAME="E4:66"/>
<font color="Maroon">M1</font> <a href="matrix_1.html#K5">@</a>  <a href="matrix_6.html#R1" target="_self">commutes_with</a> <font color="Maroon">M2</font> <a href="matrix_1.html#K5">@</a> 
 <b>by </b><i/>;<br/>


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