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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">A</font>, <font color="Maroon" title="c3">C</font>, <font color="Maroon" title="c4">B</font>, <font color="Maroon" title="c5">D</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">G</font>;<br/>









<b>assume </b><a NAME="E1:68"/>
( <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">C</font> &amp; <font color="Maroon" title="c4">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">D</font> )
 ;<br/>

<a NAME="E2:68"/><b>then </b>
 <a href="group_5.html#K4" title="GROUP_5:func.4">commutators</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c4">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="group_5.html#K4" title="GROUP_5:func.4">commutators</a> <font color="Maroon" title="c3">C</font>,<font color="Maroon" title="c5">D</font>
 
<b>by </b><i><a class="ref" href="group_5.html#T55" target="_self" title="GROUP_5:th.55">Th55</a></i>;<br/>
<a NAME="E3:68"/><b>then </b>
 <a href="group_4.html#K5" title="GROUP_4:func.5">gr</a> <span class="p1">(<span class="default"><a href="group_5.html#K4" title="GROUP_5:func.4">commutators</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c4">B</font></span>)</span> is    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of  <a href="group_4.html#K5" title="GROUP_4:func.5">gr</a> <span class="p1">(<span class="default"><a href="group_5.html#K4" title="GROUP_5:func.4">commutators</a> <font color="Maroon" title="c3">C</font>,<font color="Maroon" title="c5">D</font></span>)</span>
 
<b>by </b><i><a class="ref" href="group_4.html#T41" title="GROUP_4:th.41">GROUP_4:41</a></i>;<br/>
<a NAME="E4:68"/><b>then </b>
<span class="p1"><a href="group_5.html#K7" title="GROUP_5:func.7">[.</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c4">B</font></span><a href="group_5.html#K7" title="GROUP_5:func.7">.]</a></span> is    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of  <a href="group_4.html#K5" title="GROUP_4:func.5">gr</a> <span class="p1">(<span class="default"><a href="group_5.html#K4" title="GROUP_5:func.4">commutators</a> <font color="Maroon" title="c3">C</font>,<font color="Maroon" title="c5">D</font></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E5:68"/>
<span class="p1"><a href="group_5.html#K7" title="GROUP_5:func.7">[.</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c4">B</font></span><a href="group_5.html#K7" title="GROUP_5:func.7">.]</a></span> is    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <span class="p1"><a href="group_5.html#K7" title="GROUP_5:func.7">[.</a><span class="default"><font color="Maroon" title="c3">C</font>,<font color="Maroon" title="c5">D</font></span><a href="group_5.html#K7" title="GROUP_5:func.7">.]</a></span>
 ;<br/>


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