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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="classes2.html#NM1">Universe</a>;<br/>

<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="grcat_1.html#K28" target="_self">GroupCat</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="grcat_1.html#K19" target="_self">GroupObjects</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font></span>)</span>;<br/>

<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></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">c<sub>1</sub></font></span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font></span>)</span> ;<br/>
<i><font color="Green">E54</font></i>:  <a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>7</sub></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">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="grcat_1.html#D32" target="_self">Def32</a></i>
;<br/>
 <a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>4</sub></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">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>6</sub></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">c<sub>6</sub></font>
<b>by </b><i><a class="ref" href="grcat_1.html#D33" target="_self">Def33</a></i>
;<br/>
<b>hence </b><a NAME="E5:94"/>
( <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> the <a href="cat_1.html#U5">Comp</a> of <span class="p1">(<span class="default"><a href="grcat_1.html#K28" target="_self">GroupCat</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> iff  <a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="grcat_1.html#E3:94"><i><font color="Green">E54</font></i></a>, <a class="ref" href="grcat_1.html#D35" target="_self">Def35</a></i>;<br/>


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