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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>







<b>assume </b><a NAME="E1:39"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="nattra_1.html#R2" target="_self">is_naturally_transformable_to</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E2:39"/><b>then </b><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="nattra_1.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="nattra_1.html#D7" target="_self">Def7</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="nattra_1.html#M2" target="_self">natural_transformation</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="nattra_1.html#K7" target="_self">id</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nattra_1.html#K8" target="_self">`*`</a> <font color="Maroon">c<sub>5</sub></font> = 
<span class="p1">(<span class="default"><a href="nattra_1.html#K7" target="_self">id</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nattra_1.html#K6" target="_self">`*`</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="nattra_1.html#E1:39"><i><font color="Green">E32</font></i></a>, <a class="ref" href="nattra_1.html#D9" target="_self">Def9</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="nattra_1.html#E2:39"><i><font color="Green">E33</font></i></a>, <a class="ref" href="nattra_1.html#T22" target="_self">Th22</a></i>
;<br/>

<b>thus </b><font color="Maroon">c<sub>5</sub></font> <a href="nattra_1.html#K8" target="_self">`*`</a> <span class="p1">(<span class="default"><a href="nattra_1.html#K7" target="_self">id</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<font color="Maroon">c<sub>5</sub></font> <a href="nattra_1.html#K6" target="_self">`*`</a> <span class="p1">(<span class="default"><a href="nattra_1.html#K7" target="_self">id</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="nattra_1.html#E1:39"><i><font color="Green">E32</font></i></a>, <a class="ref" href="nattra_1.html#D9" target="_self">Def9</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="nattra_1.html#E2:39"><i><font color="Green">E33</font></i></a>, <a class="ref" href="nattra_1.html#T22" target="_self">Th22</a></i>
;<br/>


</div>
