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<b>let </b><font color="Maroon">C</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">D</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>, <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">f</font> be    <a href="cat_1.html#M1">Morphism</a> of <font color="Maroon">c</font>,<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">D</font>, <font color="Maroon">d'</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">g</font> be    <a href="cat_1.html#M1">Morphism</a> of <font color="Maroon">d</font>,<font color="Maroon">d'</font>;<br/>











<b>assume </b><a NAME="E1:46"/>
(  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">c</font>,<font color="Maroon">c'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">d</font>,<font color="Maroon">d'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/>

<a NAME="E2:46"/><b>then </b>
(  <a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp;  <a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c'</font> &amp;  <a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp;  <a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d'</font> )
 
<b>by </b><i><a class="ref" href="cat_1.html#T23">CAT_1:23</a></i>;<br/>
<a NAME="E3:46"/><b>then </b>
(  <a href="cat_1.html#K2">dom</a> <span class="p1"><a href="cat_2.html#K13" target="_self">[</a><span class="default"><font color="Maroon">f</font>,<font color="Maroon">g</font></span><a href="cat_2.html#K13" target="_self">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="cat_2.html#K12" target="_self">[</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">d</font></span><a href="cat_2.html#K12" target="_self">]</a></span> &amp;  <a href="cat_1.html#K3">cod</a> <span class="p1"><a href="cat_2.html#K13" target="_self">[</a><span class="default"><font color="Maroon">f</font>,<font color="Maroon">g</font></span><a href="cat_2.html#K13" target="_self">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="cat_2.html#K12" target="_self">[</a><span class="default"><font color="Maroon">c'</font>,<font color="Maroon">d'</font></span><a href="cat_2.html#K12" target="_self">]</a></span> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:46"/>
<span class="p1"><a href="cat_2.html#K13" target="_self">[</a><span class="default"><font color="Maroon">f</font>,<font color="Maroon">g</font></span><a href="cat_2.html#K13" target="_self">]</a></span> is    <a href="cat_1.html#M1">Morphism</a> of <span class="p1"><a href="cat_2.html#K12" target="_self">[</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">d</font></span><a href="cat_2.html#K12" target="_self">]</a></span>,<span class="p1"><a href="cat_2.html#K12" target="_self">[</a><span class="default"><font color="Maroon">c'</font>,<font color="Maroon">d'</font></span><a href="cat_2.html#K12" target="_self">]</a></span>
 <b>by </b><i><a class="ref" href="cat_1.html#T22">CAT_1:22</a></i>;<br/>


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