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<b>let </b><font color="Maroon" title="c1">H</font>, <font color="Maroon" title="c2">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/><b>let </b><font color="Maroon" title="c3">g</font> be   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c1">H</font>;<br/>





<b>assume </b><a NAME="E1:67"/>
<font color="Maroon" title="c2">G</font> is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>
 ;<br/>

<a NAME="E2:67"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">G</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
<b>by </b><i><a class="ref" href="struct_0.html#D11" title="STRUCT_0:def.11">STRUCT_0:def 11</a></i>;<br/>
<a NAME="E3:67"/><b>then </b>
<font color="Maroon" title="c3">g</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">G</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
<b>by </b><i><a class="ref" href="finset_1.html#T17" title="FINSET_1:th.17">FINSET_1:17</a></i>;<br/>
<a NAME="E4:67"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="group_6.html#K12" title="GROUP_6:func.12">Image</a> <font color="Maroon" title="c3">g</font></span>)</span> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
<b>by </b><i><a class="ref" href="group_6.html#D11" target="_self" title="GROUP_6:def.11">Def11</a></i>;<br/>
<b>hence </b><a NAME="E5:67"/>
 <a href="group_6.html#K12" title="GROUP_6:func.12">Image</a> <font color="Maroon" title="c3">g</font> is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>
 <b>by </b><i><a class="ref" href="struct_0.html#D11" title="STRUCT_0:def.11">STRUCT_0:def 11</a></i>;<br/>


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