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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="group_1.html#V2">unital</a> <a href="group_1.html#V4">associative</a> <a href="group_1.html#V7">commutative</a>  <a href="group_1.html#L1">HGrStr</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM7">FinSequence</a> of <font color="Maroon">L</font>, <font color="Maroon">g</font> be   <a href="struct_0.html#NM7">FinSequence</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="funct_2.html#NM2">Permutation</a> of  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">f</font>;<br/>





<b>assume </b><a NAME="E1:25"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">p</font>
 ;<br/>

<b>set </b><font color="Maroon">mL</font> = the <a href="group_1.html#U1">mult</a> of <font color="Maroon">L</font>;<br/>
<a NAME="E2:25"/><i><font color="Green">E43</font></i>: 
the <a href="group_1.html#U1">mult</a> of <font color="Maroon">L</font> is <a href="binop_1.html#V1">commutative</a>
 
<b>by </b><i><a class="ref" href="monoid_0.html#D11">MONOID_0:def 11</a></i>;<br/>
<a NAME="E3:25"/><i><font color="Green">E44</font></i>: 
the <a href="group_1.html#U1">mult</a> of <font color="Maroon">L</font> is <a href="binop_1.html#V2">associative</a>
 
<b>by </b><i><a class="ref" href="group_1.html#T31">GROUP_1:31</a></i>;<br/>
<a NAME="E4:25"/><i><font color="Green">E45</font></i>: 
the <a href="group_1.html#U1">mult</a> of <font color="Maroon">L</font> <a href="setwiseo.html#NR1" target="_self">has_a_unity</a> 
 
<b>by </b><i><a class="ref" href="group_1.html#T34">GROUP_1:34</a></i>;<br/>
<b>thus </b> <a href="group_4.html#K3">Product</a> <font color="Maroon">g</font> = 
the <a href="group_1.html#U1">mult</a> of <font color="Maroon">L</font> <a href="finsop_1.html#K2">$$</a> <font color="Maroon">g</font>
<b>by </b><i><a class="ref" href="group_4.html#D3">GROUP_4:def 3</a></i>
<br/>.= 
the <a href="group_1.html#U1">mult</a> of <font color="Maroon">L</font> <a href="finsop_1.html#K2">$$</a> <font color="Maroon">f</font>
<b>by </b><i>, , , , <a class="ref" href="finsop_1.html#T8">FINSOP_1:8</a></i>
<br/>.= 
 <a href="group_4.html#K3">Product</a> <font color="Maroon">f</font>
<b>by </b><i><a class="ref" href="group_4.html#D3">GROUP_4:def 3</a></i>
;<br/>


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