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

<span class="kw">let </span><font color="Maroon" title="c1">G</font>, <font color="Maroon" title="c2">H</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">g</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font>  st <font color="Maroon" title="c1">G</font> is  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>  holds <br/> <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Olive" title="b1">g</font> is  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> </span><br/><span class="kw">let </span><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="c1">G</font>,<font color="Maroon" title="c2">H</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">G</font> is  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>  implies  <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">g</font> is  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>  )</span><br/>





<span class="kw">assume </span><a NAME="E1:72"/>
<font color="Maroon" title="c1">G</font> is  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">g</font> is  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> </span><br/>

<a NAME="E2:72"/><span class="kw">then </span>
<font color="Maroon" title="c3">g</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E3:72"/>
 <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c3">g</font> is  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#D10" target="_self" onmouseover="rs('group_6/D10')" onmouseout="rh()">Def10</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
