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<b>let </b><font color="Maroon">B</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">F</font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">A</font>;<br/>







<b>given </b><font color="Maroon">g</font> being   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">A</font><b> such that </b><a NAME="E1:2"/><i><font color="Green">E18</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> &amp;  <a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">f</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font></span>)</span> &amp; <font color="Maroon">g</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_1.html#D12">CAT_1:def 12</a><br/>

<b>take </b>
<font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_1.html#D12">CAT_1:def 12</a><br/>

<b>thus </b><a NAME="E2:2"/>
(  <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span> &amp;  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="cat_1.html#T99">CAT_1:99</a></i>;<br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font></span>)</span> = 
<font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">g</font></span>)</span>
<b>by </b><i>, <a class="ref" href="cat_1.html#T99">CAT_1:99</a></i>
<br/>.= 
 <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="cat_1.html#T98">CAT_1:98</a></i>
;<br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span> = 
<font color="Maroon">F</font> <a href="funct_2.html#K3">.</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>
<b>by </b><i>, <a class="ref" href="cat_1.html#T99">CAT_1:99</a></i>
<br/>.= 
 <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="cat_1.html#T98">CAT_1:98</a></i>
;<br/>


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