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<b>let </b><font color="Maroon">G1</font> be   <a href="group_1.html#NM1">Group</a>, <font color="Maroon">G2</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="group_6.html#NM2">Homomorphism</a> of <font color="Maroon">G1</font>,<font color="Maroon">G2</font>;<br/><b>let </b><font color="Maroon">H1</font> be    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G2</font>, <font color="Maroon">H2</font> be    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G2</font>;<br/><b>let </b><font color="Maroon">H3</font> be    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G1</font>, <font color="Maroon">H4</font> be    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G1</font>;<br/>







<b>assume </b><a NAME="E1:9"/><i><font color="Green">E23</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> )
 ;<br/>

<b>assume </b><a NAME="E2:9"/>
<font color="Maroon">H1</font> is    <a href="group_6.html#M1">Subgroup</a> of <font color="Maroon">H2</font>
 ;<br/>

<a NAME="E3:9"/><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>
 
<b>by </b><i><a class="ref" href="group_2.html#D5">GROUP_2:def 5</a></i>;<br/>
<a NAME="E4:9"/><b>then </b>
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>
 
<b>by </b><i>, <a class="ref" href="relat_1.html#T178">RELAT_1:178</a></i>;<br/>
<b>hence </b><a NAME="E5:9"/>
<font color="Maroon">H3</font> is    <a href="group_6.html#M1">Subgroup</a> of <font color="Maroon">H4</font>
 <b>by </b><i><a class="ref" href="group_2.html#T66">GROUP_2:66</a></i>;<br/>


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