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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:52"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="cat_1.html#V7">initial</a>
 <b>and </b><br/><a NAME="E2:52"/><i><font color="Green">E30</font></i>: 
(  <a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="cat_1.html#M1">Morphism</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font><b> such that </b><br/><a NAME="E4:52"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="cat_1.html#M1">Morphism</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> holds <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="cat_3.html#E1:52"><i><font color="Green">E29</font></i></a>, <a class="ref" href="cat_1.html#D16">CAT_1:def 16</a></i>;<br/>
<a NAME="E5:52"/>
<font color="Maroon">c<sub>4</sub></font> is    <a href="cat_1.html#M1">Morphism</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="cat_3.html#E2:52"><i><font color="Green">E30</font></i></a>, <a class="ref" href="cat_1.html#T22">CAT_1:22</a></i>;<br/>
<b>hence </b><font color="Maroon">c<sub>4</sub></font> = 
<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="cat_3.html#E4:52"><i><font color="Green">E31</font></i></a></i>
<br/>.= 
 <a href="cat_3.html#K11" target="_self">init</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="cat_3.html#E4:52"><i><font color="Green">E31</font></i></a></i>
;<br/><br/>


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