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<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/><b>let </b><font color="Maroon" title="c2">F1</font>, <font color="Maroon" title="c3">F2</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font>;<br/>





<b>set </b><font color="Maroon" title="c4">g</font> = the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">G</font>;<br/>
<b>assume </b><a NAME="E1:21"/>
<font color="Maroon" title="c1">G</font> is  <a href="group_1.html#V7" title="GROUP_1:attr.7">commutative</a> <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>
 ;<br/>

<a NAME="E2:21"/><b>then </b><i><font color="Green" title="E14">A1</font></i>: 
( the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">G</font> is <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a> &amp; the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">G</font> <a href="setwiseo.html#NR1" title="SETWISEO:NR.1">has_a_unity</a>  &amp; the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">G</font> is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> )
 
<b>by </b><i><a class="ref" href="group_1.html#T31" title="GROUP_1:th.31">GROUP_1:31</a>, <a class="ref" href="group_1.html#T34" title="GROUP_1:th.34">GROUP_1:34</a>, <a class="ref" href="group_3.html#T2" title="GROUP_3:th.2">GROUP_3:2</a></i>;<br/>
<b>let </b><font color="Maroon" title="c5">P</font> be   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">F1</font>;<br/>

<b>assume </b><a NAME="E3:21"/><i><font color="Green" title="E15">A2</font></i>: 
<font color="Maroon" title="c3">F2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F1</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c5">P</font>
 ;<br/>

<b>thus </b><a NAME="E4:21"/>
 <a href="group_4.html#K3" title="GROUP_4:func.3">Product</a> <font color="Maroon" title="c2">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_4.html#K3" title="GROUP_4:func.3">Product</a> <font color="Maroon" title="c3">F2</font>
 <b>by </b><i><a class="txt" href="group_4.html#E2:21"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="group_4.html#E3:21"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="finsop_1.html#T8" title="FINSOP_1:th.8">FINSOP_1:8</a></i>;<br/>


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