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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be   <a href="cat_1.html#NM4" title="CAT_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="cat_1.html#M2" title="CAT_1: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="nattra_1.html#M2" title="NATTRA_1: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="nattra_1.html#M2" title="NATTRA_1: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="E1:40"/><i><font color="Green" title="E34">A1</font></i>: 
<font color="Maroon" title="c3">F</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c4">F1</font>
 <b>and </b><br/><a NAME="E2:40"/><i><font color="Green" title="E35">A2</font></i>: 
<font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font>
 <b>and </b><br/><a NAME="E3:40"/><i><font color="Green" title="E36">A3</font></i>: 
<font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c6">F3</font>
 ;<br/>

<a NAME="E4:40"/><i><font color="Green" title="E37">A4</font></i>: 
<font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c6">F3</font>
 
<b>by </b><i><a class="txt" href="nattra_1.html#E2:40"><i><font color="Green" title="E35">A2</font></i></a>, <a class="txt" href="nattra_1.html#E3:40"><i><font color="Green" title="E36">A3</font></i></a>, <a class="ref" href="nattra_1.html#T25" target="_self" title="NATTRA_1:th.25">Th25</a></i>;<br/>
<a NAME="E5:40"/><i><font color="Green" title="E38">A5</font></i>: 
<font color="Maroon" title="c3">F</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font>
 
<b>by </b><i><a class="txt" href="nattra_1.html#E1:40"><i><font color="Green" title="E34">A1</font></i></a>, <a class="txt" href="nattra_1.html#E2:40"><i><font color="Green" title="E35">A2</font></i></a>, <a class="ref" href="nattra_1.html#T25" target="_self" title="NATTRA_1:th.25">Th25</a></i>;<br/>
<a NAME="E6:40"/><i><font color="Green" title="E39">A6</font></i>: 
( <font color="Maroon" title="c3">F</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c4">F1</font> &amp; <font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c5">F2</font> &amp; <font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c6">F3</font> )
 
<b>by </b><i><a class="txt" href="nattra_1.html#E1:40"><i><font color="Green" title="E34">A1</font></i></a>, <a class="txt" href="nattra_1.html#E2:40"><i><font color="Green" title="E35">A2</font></i></a>, <a class="txt" href="nattra_1.html#E3:40"><i><font color="Green" title="E36">A3</font></i></a>, <a class="ref" href="nattra_1.html#D7" target="_self" title="NATTRA_1:def.7">Def7</a></i>;<br/>
<b>let </b><font color="Maroon" title="c9">t3</font> be    <a href="nattra_1.html#M2" title="NATTRA_1: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="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c8">t1</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c7">t</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">t3</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c8">t1</font></span>)</span> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c7">t</font>
<b>by </b><i><a class="txt" href="nattra_1.html#E1:40"><i><font color="Green" title="E34">A1</font></i></a>, <a class="txt" href="nattra_1.html#E4:40"><i><font color="Green" title="E37">A4</font></i></a>, <a class="ref" href="nattra_1.html#D9" target="_self" title="NATTRA_1:def.9">Def9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">t3</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c8">t1</font></span>)</span> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c7">t</font>
<b>by </b><i><a class="txt" href="nattra_1.html#E2:40"><i><font color="Green" title="E35">A2</font></i></a>, <a class="txt" href="nattra_1.html#E3:40"><i><font color="Green" title="E36">A3</font></i></a>, <a class="ref" href="nattra_1.html#D9" target="_self" title="NATTRA_1:def.9">Def9</a></i>
<br/>.= 
<font color="Maroon" title="c9">t3</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">t1</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <font color="Maroon" title="c7">t</font></span>)</span>
<b>by </b><i><a class="txt" href="nattra_1.html#E6:40"><i><font color="Green" title="E39">A6</font></i></a>, <a class="ref" href="nattra_1.html#T23" target="_self" title="NATTRA_1:th.23">Th23</a></i>
<br/>.= 
<font color="Maroon" title="c9">t3</font> <a href="nattra_1.html#K6" title="NATTRA_1:func.6">`*`</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">t1</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c7">t</font></span>)</span>
<b>by </b><i><a class="txt" href="nattra_1.html#E1:40"><i><font color="Green" title="E34">A1</font></i></a>, <a class="txt" href="nattra_1.html#E2:40"><i><font color="Green" title="E35">A2</font></i></a>, <a class="ref" href="nattra_1.html#D9" target="_self" title="NATTRA_1:def.9">Def9</a></i>
<br/>.= 
<font color="Maroon" title="c9">t3</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">t1</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c7">t</font></span>)</span>
<b>by </b><i><a class="txt" href="nattra_1.html#E3:40"><i><font color="Green" title="E36">A3</font></i></a>, <a class="txt" href="nattra_1.html#E5:40"><i><font color="Green" title="E38">A5</font></i></a>, <a class="ref" href="nattra_1.html#D9" target="_self" title="NATTRA_1:def.9">Def9</a></i>
;<br/>


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