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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>reconsider </b><font color="Maroon">i</font> =  <a href="partfun1.html#K6">id</a> <font color="Maroon">X</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="monoid_0.html#K18" target="_self">GPerms</a> <font color="Maroon">X</font></span>)</span> <b>by </b><i><a class="txt" href="monoid_0.html#E42"><i><font color="Green">Lemma71</font></i></a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="152_1"><b>now </b></a><div class="add"><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="monoid_0.html#K18" target="_self">GPerms</a> <font color="Maroon">X</font></span>)</span>;<br/><b>reconsider </b><font color="Maroon">f</font> = <font color="Maroon">a</font> as   <a href="funct_2.html#NM2">Permutation</a> of <font color="Maroon">X</font> <b>by </b><i><a class="txt" href="monoid_0.html#E42"><i><font color="Green">Lemma71</font></i></a></i>;<br/><a NAME="E2:152_1"/>
( <font color="Maroon">a</font> <a href="monoid_0.html#K2" target="_self">[*]</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="monoid_0.html#NK2" target="_self">(*)</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="monoid_0.html#K2" target="_self">[*]</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> <a href="monoid_0.html#NK2" target="_self">(*)</a> <font color="Maroon">a</font> )
 <b>by </b><i/>;<br/><a NAME="E3:152_1"/><b>then </b>
( <font color="Maroon">H<sub>2</sub></font>( <a href="monoid_0.html#K18" target="_self">GPerms</a> <font color="Maroon">X</font>) <a href="binop_1.html#K2">.</a> <font color="Maroon">a</font>,<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="monoid_0.html#NK2" target="_self">(*)</a> <font color="Maroon">i</font> &amp; <font color="Maroon">H<sub>2</sub></font>( <a href="monoid_0.html#K18" target="_self">GPerms</a> <font color="Maroon">X</font>) <a href="binop_1.html#K2">.</a> <font color="Maroon">i</font>,<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> <a href="monoid_0.html#NK2" target="_self">(*)</a> <font color="Maroon">f</font> )
 ;<br/><b>hence </b><a NAME="E4:152_1"/>
( <font color="Maroon">H<sub>2</sub></font>( <a href="monoid_0.html#K18" target="_self">GPerms</a> <font color="Maroon">X</font>) <a href="binop_1.html#K2">.</a> <font color="Maroon">i</font>,<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">H<sub>2</sub></font>( <a href="monoid_0.html#K18" target="_self">GPerms</a> <font color="Maroon">X</font>) <a href="binop_1.html#K2">.</a> <font color="Maroon">a</font>,<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 <b>by </b><i><a class="ref" href="funct_2.html#T23">FUNCT_2:23</a></i>;<br/></div><b>end;</b></div>
<a NAME="E3:152"/><b>then </b>
<font color="Maroon">i</font> <a href="binop_1.html#R3">is_a_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>( <a href="monoid_0.html#K18" target="_self">GPerms</a> <font color="Maroon">X</font>)
 
<b>by </b><i><a class="ref" href="binop_1.html#T11">BINOP_1:11</a></i>;<br/>
<b>hence </b><a NAME="E4:152"/>
 <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>( <a href="monoid_0.html#K18" target="_self">GPerms</a> <font color="Maroon">X</font>) <a href="hidden.html#R1">=</a>  <a href="partfun1.html#K6">id</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="binop_1.html#D8">BINOP_1:def 8</a></i>;<br/>

<b>hence </b><a NAME="E5:152"/>
 <a href="group_1.html#K2">1.</a> <span class="p1">(<span class="default"><a href="monoid_0.html#K18" target="_self">GPerms</a> <font color="Maroon">X</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="partfun1.html#K6">id</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="group_1.html#T33">GROUP_1:33</a></i>;<br/>


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