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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="matrix_2.html#K13">Group_of_Perm</a> <font color="Maroon">n</font></span>)</span>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="matrix_2.html#K13">Group_of_Perm</a> <font color="Maroon">n</font></span>)</span>;<br/><b>let </b><font color="Maroon">pa</font> be    <a href="matrix_2.html#M3">Element</a> of  <a href="matrix_2.html#K12">Permutations</a> <font color="Maroon">n</font>, <font color="Maroon">pb</font> be    <a href="matrix_2.html#M3">Element</a> of  <a href="matrix_2.html#K12">Permutations</a> <font color="Maroon">n</font>;<br/>





<b>assume </b><a NAME="E1:9"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">pa</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">pb</font> )
 ;<br/>

<font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font> = 
the <a href="group_1.html#U1">mult</a> of <span class="p1">(<span class="default"><a href="matrix_2.html#K13">Group_of_Perm</a> <font color="Maroon">n</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="group_1.html#D1">GROUP_1:def 1</a></i>
<br/>.= 
<font color="Maroon">pb</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">pa</font>
<b>by </b><i><a class="ref" href="matrix_2.html#D13">MATRIX_2:def 13</a>, </i>
;<br/>
<b>hence </b><a NAME="E3:9"/>
<font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">pb</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">pa</font>
 ;<br/>


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