<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">C</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#NM1">Object</a> of <font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">d</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">f</font> be    <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">a</font>,<font color="Maroon">b</font>;<br/><b>let </b><font color="Maroon">g</font> be    <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">b</font>,<font color="Maroon">c</font>;<br/><b>let </b><font color="Maroon">h</font> be    <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">c</font>,<font color="Maroon">d</font>;<br/>















<b>assume </b><b>that </b><br/><a NAME="E1:42"/><i><font color="Green">E20</font></i>: 
 <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>and </b><br/><a NAME="E2:42"/><i><font color="Green">E21</font></i>: 
 <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>and </b><br/><a NAME="E3:42"/><i><font color="Green">E22</font></i>: 
 <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>reconsider </b><font color="Maroon">ff</font> = <font color="Maroon">f</font> as   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">C</font> ;<br/>
<b>reconsider </b><font color="Maroon">gg</font> = <font color="Maroon">g</font> as   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">C</font> ;<br/>
<b>reconsider </b><font color="Maroon">hh</font> = <font color="Maroon">h</font> as   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">C</font> ;<br/>
<a NAME="E7:42"/>
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> &amp; <font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> &amp; <font color="Maroon">h</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">c</font>,<font color="Maroon">d</font> )
 
<b>by </b><i>, , , </i>;<br/>
<a NAME="E8:42"/><b>then </b><i><font color="Green">E23</font></i>: 
(  <a href="cat_1.html#K2" target="_self">dom</a> <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp;  <a href="cat_1.html#K3" target="_self">cod</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp;  <a href="cat_1.html#K2" target="_self">dom</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp;  <a href="cat_1.html#K3" target="_self">cod</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E9:42"/><i><font color="Green">E50</font></i>: 
 <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, , <a class="ref" href="cat_1.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E10:42"/>
 <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">b</font>,<font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, , <a class="ref" href="cat_1.html#T8" target="_self">Th8</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="cat_1.html#K9" target="_self">*</a> <font color="Maroon">g</font></span>)</span> <a href="cat_1.html#K9" target="_self">*</a> <font color="Maroon">f</font> = 
<span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="cat_1.html#K9" target="_self">*</a> <font color="Maroon">g</font></span>)</span> <a href="cat_1.html#K4" target="_self">*</a> <font color="Maroon">ff</font>
<b>by </b><i>, <a class="ref" href="cat_1.html#T9" target="_self">Th9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">hh</font> <a href="cat_1.html#K4" target="_self">*</a> <font color="Maroon">gg</font></span>)</span> <a href="cat_1.html#K4" target="_self">*</a> <font color="Maroon">ff</font>
<b>by </b><i>, , <a class="ref" href="cat_1.html#T9" target="_self">Th9</a></i>
<br/>.= 
<font color="Maroon">hh</font> <a href="cat_1.html#K4" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">gg</font> <a href="cat_1.html#K4" target="_self">*</a> <font color="Maroon">ff</font></span>)</span>
<b>by </b><i>, <a class="txt" href="cat_1.html#E1:42"><i><font color="Green">E20</font></i></a></i>
<br/>.= 
<font color="Maroon">hh</font> <a href="cat_1.html#K4" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="cat_1.html#K9" target="_self">*</a> <font color="Maroon">f</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="cat_1.html#T9" target="_self">Th9</a></i>
<br/>.= 
<font color="Maroon">h</font> <a href="cat_1.html#K9" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="cat_1.html#K9" target="_self">*</a> <font color="Maroon">f</font></span>)</span>
<b>by </b><i>, <a class="ref" href="cat_1.html#D4" target="_self">Def4</a>, <a class="ref" href="cat_1.html#T9" target="_self">Th9</a></i>
;<br/><br/>


</div>
