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<b>let </b><font color="Maroon">G1</font> be  <a href="group_1.html#V1">strict</a>  <a href="group_1.html#L1">HGrStr</a> , <font color="Maroon">G2</font> be  <a href="group_1.html#V1">strict</a>  <a href="group_1.html#L1">HGrStr</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:41_1_2"/><i><font color="Green">E54</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G1</font> <a href="hidden.html#R1">=</a>  <a href="matrix_2.html#K12" target="_self">Permutations</a> <font color="Maroon">n</font>
 <b>and </b><br/><a NAME="E2:41_1_2"/><i><font color="Green">E55</font></i>: 
for <font color="Olive">q</font>, <font color="Olive">p</font> being   <a href="matrix_2.html#M3" target="_self">Element</a> of  <a href="matrix_2.html#K12" target="_self">Permutations</a> <font color="Maroon">n</font> holds  the <a href="group_1.html#U1">mult</a> of <font color="Maroon">G1</font> <a href="binop_1.html#K1">.</a> <font color="Olive">q</font>,<font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Olive">p</font> <a href="partfun1.html#K1">*</a> <font color="Olive">q</font>
 <b>and </b><br/><a NAME="E3:41_1_2"/><i><font color="Green">E61</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G2</font> <a href="hidden.html#R1">=</a>  <a href="matrix_2.html#K12" target="_self">Permutations</a> <font color="Maroon">n</font>
 <b>and </b><br/><a NAME="E4:41_1_2"/><i><font color="Green">E62</font></i>: 
for <font color="Olive">q</font>, <font color="Olive">p</font> being   <a href="matrix_2.html#M3" target="_self">Element</a> of  <a href="matrix_2.html#K12" target="_self">Permutations</a> <font color="Maroon">n</font> holds  the <a href="group_1.html#U1">mult</a> of <font color="Maroon">G2</font> <a href="binop_1.html#K1">.</a> <font color="Olive">q</font>,<font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Olive">p</font> <a href="partfun1.html#K1">*</a> <font color="Olive">q</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">q</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G1</font>, <font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G1</font>;<br/><b>reconsider </b><font color="Maroon">q'</font> = <font color="Maroon">q</font>, <font color="Maroon">p'</font> = <font color="Maroon">p</font> as    <a href="matrix_2.html#M3" target="_self">Element</a> of  <a href="matrix_2.html#K12" target="_self">Permutations</a> <font color="Maroon">n</font> <b>by </b><i/>;<br/><b>thus </b>the <a href="group_1.html#U1">mult</a> of <font color="Maroon">G1</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">q</font>,<font color="Maroon">p</font> = 
<font color="Maroon">p'</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">q'</font>
<b>by </b><i/>
<br/>.= 
the <a href="group_1.html#U1">mult</a> of <font color="Maroon">G2</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">q</font>,<font color="Maroon">p</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:41_1_2"/>
<font color="Maroon">G1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G2</font>
 <b>by </b><i>, , <a class="ref" href="binop_1.html#T2">BINOP_1:2</a></i>;<br/>


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