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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be   <a href="altcat_1.html#NM4" title="ALTCAT_1:NM.4">category</a>;<br/><b>let </b><font color="Maroon" title="c3">F</font>, <font color="Maroon" title="c4">F1</font>, <font color="Maroon" title="c5">F2</font>, <font color="Maroon" title="c6">F3</font> be  <a href="functor0.html#V15" title="FUNCTOR0:attr.15">covariant</a>  <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>;<br/><b>let </b><font color="Maroon" title="c7">t</font> be    <a href="functor2.html#M2" title="FUNCTOR2:mode.2">natural_transformation</a> of <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">F1</font>;<br/><b>let </b><font color="Maroon" title="c8">t1</font> be    <a href="functor2.html#M2" title="FUNCTOR2:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:24"/><i><font color="Green" title="E19">A1</font></i>: 
<font color="Maroon" title="c3">F</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c4">F1</font>
 <b>and </b><br/><a NAME="E2:24"/><i><font color="Green" title="E20">A2</font></i>: 
<font color="Maroon" title="c4">F1</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font>
 <b>and </b><br/><a NAME="E3:24"/><i><font color="Green" title="E21">A3</font></i>: 
<font color="Maroon" title="c5">F2</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c6">F3</font>
 ;<br/>

<a NAME="E4:24"/><i><font color="Green" title="E22">A4</font></i>: 
<font color="Maroon" title="c4">F1</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c6">F3</font>
 
<b>by </b><i><a class="txt" href="functor2.html#E2:24"><i><font color="Green" title="E20">A2</font></i></a>, <a class="txt" href="functor2.html#E3:24"><i><font color="Green" title="E21">A3</font></i></a>, <a class="ref" href="functor2.html#T10" target="_self" title="FUNCTOR2:th.10">Th10</a></i>;<br/>
<a NAME="E5:24"/><i><font color="Green" title="E23">A5</font></i>: 
<font color="Maroon" title="c3">F</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font>
 
<b>by </b><i><a class="txt" href="functor2.html#E1:24"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="functor2.html#E2:24"><i><font color="Green" title="E20">A2</font></i></a>, <a class="ref" href="functor2.html#T10" target="_self" title="FUNCTOR2:th.10">Th10</a></i>;<br/>
<a NAME="E6:24"/><i><font color="Green" title="E24">A6</font></i>: 
( <font color="Maroon" title="c3">F</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c4">F1</font> &amp; <font color="Maroon" title="c4">F1</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c5">F2</font> &amp; <font color="Maroon" title="c5">F2</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c6">F3</font> )
 
<b>by </b><i><a class="txt" href="functor2.html#E1:24"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="functor2.html#E2:24"><i><font color="Green" title="E20">A2</font></i></a>, <a class="txt" href="functor2.html#E3:24"><i><font color="Green" title="E21">A3</font></i></a>, <a class="ref" href="functor2.html#D6" target="_self" title="FUNCTOR2:def.6">Def6</a></i>;<br/>
<b>let </b><font color="Maroon" title="c9">t3</font> be    <a href="functor2.html#M2" title="FUNCTOR2:mode.2">natural_transformation</a> of <font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c6">F3</font>;<br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c9">t3</font> <a href="functor2.html#K5" title="FUNCTOR2:func.5">`*`</a> <font color="Maroon" title="c8">t1</font></span>)</span> <a href="functor2.html#K5" title="FUNCTOR2:func.5">`*`</a> <font color="Maroon" title="c7">t</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">t3</font> <a href="functor2.html#K5" title="FUNCTOR2:func.5">`*`</a> <font color="Maroon" title="c8">t1</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <font color="Maroon" title="c7">t</font>
<b>by </b><i><a class="txt" href="functor2.html#E1:24"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="functor2.html#E4:24"><i><font color="Green" title="E22">A4</font></i></a>, <a class="ref" href="functor2.html#D8" target="_self" title="FUNCTOR2:def.8">Def8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">t3</font> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <font color="Maroon" title="c8">t1</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <font color="Maroon" title="c7">t</font>
<b>by </b><i><a class="txt" href="functor2.html#E2:24"><i><font color="Green" title="E20">A2</font></i></a>, <a class="txt" href="functor2.html#E3:24"><i><font color="Green" title="E21">A3</font></i></a>, <a class="ref" href="functor2.html#D8" target="_self" title="FUNCTOR2:def.8">Def8</a></i>
<br/>.= 
<font color="Maroon" title="c9">t3</font> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">t1</font> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <font color="Maroon" title="c7">t</font></span>)</span>
<b>by </b><i><a class="txt" href="functor2.html#E6:24"><i><font color="Green" title="E24">A6</font></i></a>, <a class="ref" href="functor2.html#T8" target="_self" title="FUNCTOR2:th.8">Th8</a></i>
<br/>.= 
<font color="Maroon" title="c9">t3</font> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">t1</font> <a href="functor2.html#K5" title="FUNCTOR2:func.5">`*`</a> <font color="Maroon" title="c7">t</font></span>)</span>
<b>by </b><i><a class="txt" href="functor2.html#E1:24"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="functor2.html#E2:24"><i><font color="Green" title="E20">A2</font></i></a>, <a class="ref" href="functor2.html#D8" target="_self" title="FUNCTOR2:def.8">Def8</a></i>
<br/>.= 
<font color="Maroon" title="c9">t3</font> <a href="functor2.html#K5" title="FUNCTOR2:func.5">`*`</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">t1</font> <a href="functor2.html#K5" title="FUNCTOR2:func.5">`*`</a> <font color="Maroon" title="c7">t</font></span>)</span>
<b>by </b><i><a class="txt" href="functor2.html#E3:24"><i><font color="Green" title="E21">A3</font></i></a>, <a class="txt" href="functor2.html#E5:24"><i><font color="Green" title="E23">A5</font></i></a>, <a class="ref" href="functor2.html#D8" target="_self" title="FUNCTOR2:def.8">Def8</a></i>
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