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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#NM2">Morphism</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:37"/><i><font color="Green">E24</font></i>: 
 <a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>given </b><font color="Maroon">c<sub>4</sub></font> being   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><a NAME="E2:37"/><i><font color="Green">E25</font></i>: 
 <a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_1.html#K4">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E3:37"/><i><font color="Green">E26</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_1.html#K4">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="cat_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></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> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_1.html#K4">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_3.html#D10" target="_self">CAT_3:def 10</a><br/>

<b>take </b>
<font color="Maroon">c<sub>3</sub></font> <a href="cat_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_3.html#D10" target="_self">CAT_3:def 10</a><br/>

<a NAME="E4:37"/><i><font color="Green">E27</font></i>: 
 <a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_1.html#K4">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="cat_3.html#E1:37"><i><font color="Green">E24</font></i></a>, <a class="ref" href="cat_1.html#T42">CAT_1:42</a></i>;<br/>
<b>hence </b><a NAME="E5:37"/>
 <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cat_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="cat_3.html#E1:37"><i><font color="Green">E24</font></i></a>, <a class="txt" href="cat_3.html#E2:37"><i><font color="Green">E25</font></i></a>, <a class="ref" href="cat_1.html#T42">CAT_1:42</a></i>;<br/>

<b>thus </b><font color="Maroon">c<sub>2</sub></font> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cat_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
 <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">c<sub>2</sub></font> <a href="cat_1.html#K4">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="cat_3.html#E1:37"><i><font color="Green">E24</font></i></a>, <a class="txt" href="cat_3.html#E2:37"><i><font color="Green">E25</font></i></a>, <a class="txt" href="cat_3.html#E3:37"><i><font color="Green">E26</font></i></a>, <a class="txt" href="cat_3.html#E4:37"><i><font color="Green">E27</font></i></a>, <a class="ref" href="cat_1.html#T43">CAT_1:43</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> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="cat_3.html#E1:37"><i><font color="Green">E24</font></i></a>, <a class="ref" href="cat_1.html#T42">CAT_1:42</a></i>
;<br/>


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