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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">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>, <font color="Maroon">g</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>assume </b><a NAME="E1:99"/><i><font color="Green">E29</font></i>: 
 <a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">f'</font> = <font color="Maroon">f</font> as  <a href="grcat_1.html#V2" target="_self">strict</a>  <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> <b>by </b><i><a class="ref" href="grcat_1.html#T9" target="_self">Th9</a></i>;<br/>
<b>reconsider </b><font color="Maroon">g'</font> = <font color="Maroon">g</font> as  <a href="grcat_1.html#V2" target="_self">strict</a>  <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> <b>by </b><i><a class="ref" href="grcat_1.html#T9" target="_self">Th9</a></i>;<br/>
<a NAME="E4:99"/><i><font color="Green">E42</font></i>: 
 <a href="grcat_1.html#K21" target="_self">dom</a> <font color="Maroon">g'</font> <a href="hidden.html#R1">=</a>  <a href="grcat_1.html#K22" target="_self">cod</a> <font color="Maroon">f'</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:99"/><b>then </b><i><font color="Green">E43</font></i>: 
(  <a href="grcat_1.html#K9" target="_self">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g'</font> <a href="grcat_1.html#K15" target="_self">*</a> <font color="Maroon">f'</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="grcat_1.html#K21" target="_self">dom</a> <font color="Maroon">f'</font> &amp;  <a href="grcat_1.html#K10" target="_self">cod</a> <span class="p1">(<span class="default"><font color="Maroon">g'</font> <a href="grcat_1.html#K15" target="_self">*</a> <font color="Maroon">f'</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="grcat_1.html#K22" target="_self">cod</a> <font color="Maroon">g'</font> )
 
<b>by </b><i><a class="txt" href="grcat_1.html#E1:99"><i><font color="Green">E29</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon">gf</font> = <font color="Maroon">g'</font> <a href="grcat_1.html#K15" target="_self">*</a> <font color="Maroon">f'</font> as    <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> <b>by </b><i>, </i>;<br/>
<a NAME="E7:99"/>
<font color="Maroon">gf</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E8:99"/>
(  <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font> &amp;  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font> )
 <b>by </b><i><a class="ref" href="grcat_1.html#D13" target="_self">Def13</a>, </i>;<br/>


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