<?xml version="1.0"?>
<div class="add">

<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">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>;<br/><b>let </b><font color="Maroon" title="c3">H</font> be    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>;<br/>





<i><font color="Green" title="E77">A1</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span></span>)</span> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">H</font> = 
<span class="p1">(<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> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">H</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/>.= 
 <a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c3">H</font>
<b>by </b><i><a class="ref" href="group_2.html#T132" target="_self" title="GROUP_2:th.132">Th132</a></i>
;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</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="c2">a</font></span>)</span> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">H</font> = 
<span class="p1">(<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> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">H</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/>.= 
 <a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c3">H</font>
<b>by </b><i><a class="ref" href="group_2.html#T132" target="_self" title="GROUP_2:th.132">Th132</a></i>
;<br/>
<b>hence </b><a NAME="E3:107"/>
(  <a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c3">H</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">H</font></span>)</span> &amp;  <a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c3">H</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">H</font></span>)</span> )
 <b>by </b><i><a class="txt" href="group_2.html#E1:107"><i><font color="Green" title="E77">A1</font></i></a>, <a class="ref" href="group_2.html#T139" target="_self" title="GROUP_2:th.139">Th139</a></i>;<br/>


</div>
