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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">E</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">E</font>;<br/><b>let </b><font color="Maroon" title="c5">T</font> be   <a href="group_10.html#NM1" title="GROUP_10:NM.1">LeftOperation</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">E</font>;<br/>







<b>assume </b><a NAME="E1:26"/>
<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font> <a href="group_10.html#R2" title="GROUP_10:pred.2">are_conjugated_under</a> <font color="Maroon" title="c5">T</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c6">g</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E3:26"/><i><font color="Green" title="E18">A1</font></i>: 
<font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">T</font> <a href="group_10.html#K1" title="GROUP_10:func.1">^</a> <font color="Maroon" title="c6">g</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font>
 <b>by </b><i><a class="ref" href="group_10.html#D14" target="_self" title="GROUP_10:def.14">Def14</a></i>;<br/>
<a NAME="E4:26"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">E</font>
 
;<br/>
<a NAME="E5:26"/><b>then </b><i><font color="Green" title="E19">A2</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">T</font> <a href="group_10.html#K1" title="GROUP_10:func.1">^</a> <font color="Maroon" title="c6">g</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">T</font> <a href="group_10.html#K1" title="GROUP_10:func.1">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">T</font> <a href="group_10.html#K1" title="GROUP_10:func.1">^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">T</font> <a href="group_10.html#K1" title="GROUP_10:func.1">^</a> <font color="Maroon" title="c6">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font>
<b>by </b><i><a class="txt" href="group_10.html#E3:26"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="group_10.html#E5:26"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">T</font> <a href="group_10.html#K1" title="GROUP_10:func.1">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c6">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font>
<b>by </b><i><a class="ref" href="group_10.html#D1" target="_self" title="GROUP_10:def.1">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">T</font> <a href="group_10.html#K1" title="GROUP_10:func.1">^</a> <span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c1">G</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font>
<b>by </b><i><a class="ref" href="group_1.html#D6" title="GROUP_1:def.6">GROUP_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c2">E</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font>
<b>by </b><i><a class="ref" href="group_10.html#D1" target="_self" title="GROUP_10:def.1">Def1</a></i>
<br/>.= 
<font color="Maroon" title="c3">x</font>
<b>by </b><i><a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></i>
;<br/>
<b>hence </b><a NAME="E7:26"/>
<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c3">x</font> <a href="group_10.html#R2" title="GROUP_10:pred.2">are_conjugated_under</a> <font color="Maroon" title="c5">T</font>
 <b>by </b><i><a class="ref" href="group_10.html#D14" target="_self" title="GROUP_10:def.14">Def14</a></i>;<br/>


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