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<b>let </b><font color="Maroon">UN</font> be   <a href="classes2.html#NM1">Universe</a>;<br/>

<b>set </b><font color="Maroon">C</font> =  <a href="grcat_1.html#K28" target="_self">GroupCat</a> <font color="Maroon">UN</font>;<br/>
<b>set </b><font color="Maroon">V</font> =  <a href="grcat_1.html#K19" target="_self">GroupObjects</a> <font color="Maroon">UN</font>;<br/>
<b>set </b><font color="Maroon">X</font> =  <a href="grcat_1.html#K20" target="_self">Morphs</a> <span class="p1">(<span class="default"><a href="grcat_1.html#K19" target="_self">GroupObjects</a> <font color="Maroon">UN</font></span>)</span>;<br/>
<b>let </b><font color="Maroon">f</font> be   <a href="cat_1.html#NM2">Morphism</a> of <span class="p1">(<span class="default"><a href="grcat_1.html#K28" target="_self">GroupCat</a> <font color="Maroon">UN</font></span>)</span>;<br/><b>let </b><font color="Maroon">f'</font> be    <a href="grcat_1.html#M3" target="_self">Element</a> of  <a href="grcat_1.html#K20" target="_self">Morphs</a> <span class="p1">(<span class="default"><a href="grcat_1.html#K19" target="_self">GroupObjects</a> <font color="Maroon">UN</font></span>)</span>;<br/>



<b>assume </b><a NAME="E1:97"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f'</font>
 ;<br/>

<b>hence </b> <a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font> = 
<span class="p1">(<span class="default"><a href="grcat_1.html#K24" target="_self">dom</a> <span class="p2">(<span class="default"><a href="grcat_1.html#K19" target="_self">GroupObjects</a> <font color="Maroon">UN</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f'</font>
<b>by </b><i><a class="ref" href="cat_1.html#D2">CAT_1:def 2</a></i>
<br/>.= 
 <a href="grcat_1.html#K21" target="_self">dom</a> <font color="Maroon">f'</font>
<b>by </b><i><a class="ref" href="grcat_1.html#T6" target="_self">Th6</a></i>
;<br/><br/>

<b>thus </b> <a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font> = 
<span class="p1">(<span class="default"><a href="grcat_1.html#K25" target="_self">cod</a> <span class="p2">(<span class="default"><a href="grcat_1.html#K19" target="_self">GroupObjects</a> <font color="Maroon">UN</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f'</font>
<b>by </b><i>, <a class="ref" href="cat_1.html#D3">CAT_1:def 3</a></i>
<br/>.= 
 <a href="grcat_1.html#K22" target="_self">cod</a> <font color="Maroon">f'</font>
<b>by </b><i><a class="ref" href="grcat_1.html#T7" target="_self">Th7</a></i>
;<br/>


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