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<b>let </b><font color="Maroon">V</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">g</font> be   <a href="cat_1.html#NM2">Morphism</a> of <span class="p1">(<span class="default"><a href="ens_1.html#K12" target="_self">Ens</a> <font color="Maroon">V</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="ens_1.html#K12" target="_self">Ens</a> <font color="Maroon">V</font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:47"/><i><font color="Green">E16</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/>

<a NAME="E2:47"/>
 <a href="ens_1.html#K3" target="_self">dom</a> <span class="p1">(<span class="default"><a href="ens_1.html#K16" target="_self">@</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="ens_1.html#T7" target="_self">Th7</a>, </i>;<br/>
<a NAME="E3:47"/><b>then </b><i><font color="Green">E17</font></i>: 
 <a href="ens_1.html#K3" target="_self">dom</a> <span class="p1">(<span class="default"><a href="ens_1.html#K16" target="_self">@</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ens_1.html#K4" target="_self">cod</a> <span class="p1">(<span class="default"><a href="ens_1.html#K16" target="_self">@</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>thus </b><font color="Maroon">g</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f</font> = 
the <a href="cat_1.html#U5">Comp</a> of <span class="p1">(<span class="default"><a href="ens_1.html#K12" target="_self">Ens</a> <font color="Maroon">V</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="ens_1.html#K16" target="_self">@</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">f</font></span><a href="domain_1.html#K1">]</a></span>
<b>by </b><i><a class="ref" href="ens_1.html#T7" target="_self">Th7</a>, <a class="ref" href="cat_1.html#T41">CAT_1:41</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ens_1.html#K16" target="_self">@</a> <font color="Maroon">g</font></span>)</span> <a href="ens_1.html#K6" target="_self">*</a> <span class="p1">(<span class="default"><a href="ens_1.html#K16" target="_self">@</a> <font color="Maroon">f</font></span>)</span>
<b>by </b><i><a class="txt" href="ens_1.html#E10"><i><font color="Green">Lemma34</font></i></a>, </i>
;<br/>


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