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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="monoid_0.html#K17" title="MONOID_0:func.17">GPerms</a> <font color="Maroon" title="c1">X</font></span>)</span> holds  <font color="Olive" title="b1">f</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span><br/><b>let </b><font color="Maroon" title="c2">f</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="monoid_0.html#K17" title="MONOID_0:func.17">GPerms</a> <font color="Maroon" title="c1">X</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span><br/>



<b>reconsider </b><font color="Maroon" title="c3">g</font> = <font color="Maroon" title="c2">f</font> as   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="monoid_0.html#T86" target="_self" title="MONOID_0:th.86">Th86</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">b</font> = <font color="Maroon" title="c3">g</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a>  as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="monoid_0.html#K17" title="MONOID_0:func.17">GPerms</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="monoid_0.html#T86" target="_self" title="MONOID_0:th.86">Th86</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">b</font> = <font color="Maroon" title="c4">b</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="monoid_0.html#K17" title="MONOID_0:func.17">GPerms</a> <font color="Maroon" title="c1">X</font></span>)</span> ;<br/>
<a NAME="E4:149"/>
( <font color="Maroon" title="c3">g</font> <a href="monoid_0.html#NK2" title="MONOID_0:NK.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span> <a href="monoid_0.html#NK2" title="MONOID_0:NK.2">(*)</a> <font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">X</font> &amp;  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <span class="p1">(<span class="default"><a href="monoid_0.html#K17" title="MONOID_0:func.17">GPerms</a> <font color="Maroon" title="c1">X</font></span>)</span> &amp; <font color="Maroon" title="c2">f</font> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font> <a href="monoid_0.html#NK2" title="MONOID_0:NK.2">(*)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span> &amp; <font color="Maroon" title="c5">b</font> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span> <a href="monoid_0.html#NK2" title="MONOID_0:NK.2">(*)</a> <font color="Maroon" title="c3">g</font> )
 
<b>by </b><i><a class="ref" href="monoid_0.html#T79" target="_self" title="MONOID_0:th.79">Th79</a>, <a class="ref" href="monoid_0.html#T87" target="_self" title="MONOID_0:th.87">Th87</a>, <a class="ref" href="funct_2.html#T88" title="FUNCT_2:th.88">FUNCT_2:88</a></i>;<br/>
<b>hence </b><a NAME="E5:149"/>
<font color="Maroon" title="c2">f</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> 
 <b>by </b><i><a class="ref" href="group_1.html#D6" title="GROUP_1:def.6">GROUP_1:def 6</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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