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<b>let </b><font color="Maroon" title="c1">UN</font> be   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a>;<br/>

<b>set </b><font color="Maroon" title="c2">C</font> =  <a href="grcat_1.html#K28" title="GRCAT_1:func.28">GroupCat</a> <font color="Maroon" title="c1">UN</font>;<br/>
<b>set </b><font color="Maroon" title="c3">V</font> =  <a href="grcat_1.html#K19" title="GRCAT_1:func.19">GroupObjects</a> <font color="Maroon" title="c1">UN</font>;<br/>
<b>let </b><font color="Maroon" title="c4">f</font>, <font color="Maroon" title="c5">g</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="grcat_1.html#K28" title="GRCAT_1:func.28">GroupCat</a> <font color="Maroon" title="c1">UN</font></span>)</span>;<br/>

<b>reconsider </b><font color="Maroon" title="c6">f'</font> = <font color="Maroon" title="c4">f</font> as    <a href="grcat_1.html#M3" title="GRCAT_1:mode.3">Element</a> of  <a href="grcat_1.html#K20" title="GRCAT_1:func.20">Morphs</a> <span class="p1">(<span class="default"><a href="grcat_1.html#K19" title="GRCAT_1:func.19">GroupObjects</a> <font color="Maroon" title="c1">UN</font></span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon" title="c7">g'</font> = <font color="Maroon" title="c5">g</font> as    <a href="grcat_1.html#M3" title="GRCAT_1:mode.3">Element</a> of  <a href="grcat_1.html#K20" title="GRCAT_1:func.20">Morphs</a> <span class="p1">(<span class="default"><a href="grcat_1.html#K19" title="GRCAT_1:func.19">GroupObjects</a> <font color="Maroon" title="c1">UN</font></span>)</span> ;<br/>
<i><font color="Green" title="E54">A1</font></i>:  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">g</font> = 
<span class="p1">(<span class="default"><a href="grcat_1.html#K24" title="GRCAT_1:func.24">dom</a> <span class="p2">(<span class="default"><a href="grcat_1.html#K19" title="GRCAT_1:func.19">GroupObjects</a> <font color="Maroon" title="c1">UN</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">g'</font>
<b>by </b><i><a class="ref" href="cat_1.html#D2" title="CAT_1:def.2">CAT_1:def 2</a></i>
<br/>.= 
 <a href="grcat_1.html#K21" title="GRCAT_1:func.21">dom</a> <font color="Maroon" title="c7">g'</font>
<b>by </b><i><a class="ref" href="grcat_1.html#D32" target="_self" title="GRCAT_1:def.32">Def32</a></i>
;<br/>
 <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c4">f</font> = 
<span class="p1">(<span class="default"><a href="grcat_1.html#K25" title="GRCAT_1:func.25">cod</a> <span class="p2">(<span class="default"><a href="grcat_1.html#K19" title="GRCAT_1:func.19">GroupObjects</a> <font color="Maroon" title="c1">UN</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">f'</font>
<b>by </b><i><a class="ref" href="cat_1.html#D3" title="CAT_1:def.3">CAT_1:def 3</a></i>
<br/>.= 
 <a href="grcat_1.html#K22" title="GRCAT_1:func.22">cod</a> <font color="Maroon" title="c6">f'</font>
<b>by </b><i><a class="ref" href="grcat_1.html#D33" target="_self" title="GRCAT_1:def.33">Def33</a></i>
;<br/>
<b>hence </b><a NAME="E5:92"/>
( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c4">f</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> the <a href="cat_1.html#U5" title="CAT_1:sel.5">Comp</a> of <span class="p1">(<span class="default"><a href="grcat_1.html#K28" title="GRCAT_1:func.28">GroupCat</a> <font color="Maroon" title="c1">UN</font></span>)</span> iff  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c4">f</font> )
 <b>by </b><i><a class="txt" href="grcat_1.html#E3:92"><i><font color="Green" title="E54">A1</font></i></a>, <a class="ref" href="grcat_1.html#D35" target="_self" title="GRCAT_1:def.35">Def35</a></i>;<br/>


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