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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>set </b><font color="Maroon" title="c2">f</font> =  <a href="group_1.html#K4" title="GROUP_1:func.4">inverse_op</a> <font color="Maroon" title="c1">G</font>;<br/>
<b>let </b><font color="Maroon" title="c3">x1</font>, <font color="Maroon" title="c4">x2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_1.html#D8" title="FUNCT_1:def.8">FUNCT_1:def 8</a><br/>

<b>assume </b><a NAME="E1:14"/><i><font color="Green" title="E11">A1</font></i>: 
( <font color="Maroon" title="c3">x1</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"><a href="group_1.html#K4" title="GROUP_1:func.4">inverse_op</a> <font color="Maroon" title="c1">G</font></span>)</span> &amp; <font color="Maroon" title="c4">x2</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"><a href="group_1.html#K4" title="GROUP_1:func.4">inverse_op</a> <font color="Maroon" title="c1">G</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="group_1.html#K4" title="GROUP_1:func.4">inverse_op</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="group_1.html#K4" title="GROUP_1:func.4">inverse_op</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x2</font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c5">a</font> = <font color="Maroon" title="c3">x1</font>, <font color="Maroon" title="c6">b</font> = <font color="Maroon" title="c4">x2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> ;<br/>
<a NAME="E3:14"/>
( <span class="p1">(<span class="default"><a href="group_1.html#K4" title="GROUP_1:func.4">inverse_op</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a>  &amp; <span class="p1">(<span class="default"><a href="group_1.html#K4" title="GROUP_1:func.4">inverse_op</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a>  )
 
<b>by </b><i><a class="ref" href="group_1.html#D7" title="GROUP_1:def.7">GROUP_1:def 7</a></i>;<br/>
<b>hence </b><a NAME="E4:14"/>
<font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x2</font>
 <b>by </b><i><a class="txt" href="topgrp_1.html#E1:14"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="group_1.html#T17" title="GROUP_1:th.17">GROUP_1:17</a></i>;<br/>


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