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<b>let </b><font color="Maroon">G</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">H1</font> be    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">H2</font> be    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">H3</font> be    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">H4</font> be    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>;<br/>









<b>assume </b><a NAME="E1:60"/>
( <font color="Maroon">H1</font> is    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">H2</font> &amp; <font color="Maroon">H3</font> is    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">H4</font> )
 ;<br/>

<a NAME="E2:60"/><b>then </b>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H3</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H4</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> <a href="hidden.html#R1">=</a>  <a href="group_2.html#K7">carr</a> <font color="Maroon">H1</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> <a href="hidden.html#R1">=</a>  <a href="group_2.html#K7">carr</a> <font color="Maroon">H2</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H3</font> <a href="hidden.html#R1">=</a>  <a href="group_2.html#K7">carr</a> <font color="Maroon">H3</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H4</font> <a href="hidden.html#R1">=</a>  <a href="group_2.html#K7">carr</a> <font color="Maroon">H4</font> &amp;  <a href="group_5.html#K5" target="_self">commutators</a> <font color="Maroon">H1</font>,<font color="Maroon">H3</font> <a href="hidden.html#R1">=</a>  <a href="group_5.html#K4" target="_self">commutators</a> <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">H1</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">H3</font></span>)</span> &amp;  <a href="group_5.html#K5" target="_self">commutators</a> <font color="Maroon">H2</font>,<font color="Maroon">H4</font> <a href="hidden.html#R1">=</a>  <a href="group_5.html#K4" target="_self">commutators</a> <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">H2</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">H4</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="group_2.html#D5">GROUP_2:def 5</a></i>;<br/>
<b>hence </b><a NAME="E3:60"/>
 <a href="group_5.html#K5" target="_self">commutators</a> <font color="Maroon">H1</font>,<font color="Maroon">H3</font> <a href="tarski.html#R1">c=</a>  <a href="group_5.html#K5" target="_self">commutators</a> <font color="Maroon">H2</font>,<font color="Maroon">H4</font>
 <b>by </b><i/>;<br/>


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