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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="E1:56"/><i><font color="Green">E23</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#V4" target="_self">Orthogonal</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="matrix_6.html#R1" target="_self">is_permutable_with</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K5">@</a>  )
 ;<br/>

<a NAME="E2:56"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K5">@</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="matrix_6.html#K5" target="_self">~</a>  &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="matrix_6.html#V1" target="_self">Reversible</a> )
 
<b>by </b><i><a class="ref" href="matrix_6.html#D7" target="_self">Def7</a></i>;<br/>
<b>hence </b><a NAME="E3:56"/>
<font color="Maroon">c<sub>5</sub></font> <a href="matrix_6.html#R1" target="_self">is_permutable_with</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="matrix_6.html#E1:56"><i><font color="Green">E23</font></i></a>, <a class="ref" href="matrix_6.html#T41" target="_self">Th41</a></i>;<br/>


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