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<b>let </b><font color="Maroon">A</font> be   <a href="altcat_1.html#NM4">category</a>, <font color="Maroon">B</font> be   <a href="altcat_1.html#NM4">category</a>;<br/><b>let </b><font color="Maroon">F</font> be  <a href="functor0.html#V15">covariant</a>  <a href="functor0.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>, <font color="Maroon">F1</font> be  <a href="functor0.html#V15">covariant</a>  <a href="functor0.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>, <font color="Maroon">F2</font> be  <a href="functor0.html#V15">covariant</a>  <a href="functor0.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>, <font color="Maroon">F3</font> be  <a href="functor0.html#V15">covariant</a>  <a href="functor0.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>;<br/><b>let </b><font color="Maroon">t</font> be    <a href="functor2.html#M2" target="_self">natural_transformation</a> of <font color="Maroon">F</font>,<font color="Maroon">F1</font>;<br/><b>let </b><font color="Maroon">t1</font> be    <a href="functor2.html#M2" target="_self">natural_transformation</a> of <font color="Maroon">F1</font>,<font color="Maroon">F2</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:24"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">F</font> <a href="functor2.html#R2" target="_self">is_naturally_transformable_to</a> <font color="Maroon">F1</font>
 <b>and </b><br/><a NAME="E2:24"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">F1</font> <a href="functor2.html#R2" target="_self">is_naturally_transformable_to</a> <font color="Maroon">F2</font>
 <b>and </b><br/><a NAME="E3:24"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">F2</font> <a href="functor2.html#R2" target="_self">is_naturally_transformable_to</a> <font color="Maroon">F3</font>
 ;<br/>

<a NAME="E4:24"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">F1</font> <a href="functor2.html#R2" target="_self">is_naturally_transformable_to</a> <font color="Maroon">F3</font>
 
<b>by </b><i><a class="txt" href="functor2.html#E1:24"><i><font color="Green">E20</font></i></a>, , </i>;<br/>
<a NAME="E5:24"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">F</font> <a href="functor2.html#R2" target="_self">is_naturally_transformable_to</a> <font color="Maroon">F2</font>
 
<b>by </b><i>, <a class="txt" href="functor2.html#E1:24"><i><font color="Green">E20</font></i></a>, </i>;<br/>
<a NAME="E6:24"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">F</font> <a href="functor2.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">F1</font> &amp; <font color="Maroon">F1</font> <a href="functor2.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">F2</font> &amp; <font color="Maroon">F2</font> <a href="functor2.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">F3</font> )
 
<b>by </b><i>, <a class="txt" href="functor2.html#E1:24"><i><font color="Green">E20</font></i></a>, , </i>;<br/>
<b>let </b><font color="Maroon">t3</font> be    <a href="functor2.html#M2" target="_self">natural_transformation</a> of <font color="Maroon">F2</font>,<font color="Maroon">F3</font>;<br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">t3</font> <a href="functor2.html#K5" target="_self">`*`</a> <font color="Maroon">t1</font></span>)</span> <a href="functor2.html#K5" target="_self">`*`</a> <font color="Maroon">t</font> = 
<span class="p1">(<span class="default"><font color="Maroon">t3</font> <a href="functor2.html#K5" target="_self">`*`</a> <font color="Maroon">t1</font></span>)</span> <a href="functor2.html#K3" target="_self">`*`</a> <font color="Maroon">t</font>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">t3</font> <a href="functor2.html#K3" target="_self">`*`</a> <font color="Maroon">t1</font></span>)</span> <a href="functor2.html#K3" target="_self">`*`</a> <font color="Maroon">t</font>
<b>by </b><i><a class="txt" href="functor2.html#E1:24"><i><font color="Green">E20</font></i></a>, , </i>
<br/>.= 
<font color="Maroon">t3</font> <a href="functor2.html#K3" target="_self">`*`</a> <span class="p1">(<span class="default"><font color="Maroon">t1</font> <a href="functor2.html#K3" target="_self">`*`</a> <font color="Maroon">t</font></span>)</span>
<b>by </b><i><a class="ref" href="functor2.html#T4" target="_self">Th4</a>, </i>
<br/>.= 
<font color="Maroon">t3</font> <a href="functor2.html#K3" target="_self">`*`</a> <span class="p1">(<span class="default"><font color="Maroon">t1</font> <a href="functor2.html#K5" target="_self">`*`</a> <font color="Maroon">t</font></span>)</span>
<b>by </b><i>, <a class="txt" href="functor2.html#E1:24"><i><font color="Green">E20</font></i></a>, </i>
<br/>.= 
<font color="Maroon">t3</font> <a href="functor2.html#K5" target="_self">`*`</a> <span class="p1">(<span class="default"><font color="Maroon">t1</font> <a href="functor2.html#K5" target="_self">`*`</a> <font color="Maroon">t</font></span>)</span>
<b>by </b><i>, <a class="ref" href="functor2.html#D1" target="_self">Def1</a>, </i>
;<br/>


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