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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> 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="E1:6"/>
( <font color="Maroon">c<sub>3</sub></font> is <a href="matrix_8.html#V1" target="_self">Idempotent</a> &amp; <font color="Maroon">c<sub>4</sub></font> is <a href="matrix_8.html#V1" target="_self">Idempotent</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="matrix_6.html#R1">is_permutable_with</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>

<a NAME="E2:6"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="matrix_6.html#K4">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="matrix_6.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K4">*</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="matrix_8.html#D1" target="_self">Def1</a>, <a class="ref" href="matrix_6.html#D1">MATRIX_6:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:6"/>
<font color="Maroon">c<sub>3</sub></font> <a href="matrix_6.html#K4">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="matrix_6.html#R1">is_permutable_with</a> <font color="Maroon">c<sub>4</sub></font> <a href="matrix_6.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="matrix_6.html#D1">MATRIX_6:def 1</a></i>;<br/>


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