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<b>let </b><font color="Maroon">A</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">B</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">C</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">F1</font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>, <font color="Maroon">G1</font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>;<br/><b>let </b><font color="Maroon">F2</font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">C</font>, <font color="Maroon">G2</font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">C</font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:57"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">F1</font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Maroon">G1</font>
 <b>and </b><br/><a NAME="E2:57"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">F2</font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Maroon">G2</font>
 ;<br/>

<a NAME="E3:57"/>
( <font color="Maroon">F1</font> <a href="nattra_1.html#R1">is_transformable_to</a> <font color="Maroon">G1</font> &amp; <font color="Maroon">F2</font> <a href="nattra_1.html#R1">is_transformable_to</a> <font color="Maroon">G2</font> )
 
<b>by </b><i>, , <a class="ref" href="nattra_1.html#D7">NATTRA_1:def 7</a></i>;<br/>
<b>hence </b><a NAME="E4:57"/>
<span class="p1"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">F1</font>,<font color="Maroon">F2</font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <a href="nattra_1.html#R1">is_transformable_to</a> <span class="p1"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">G1</font>,<font color="Maroon">G2</font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span>
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="nattra_1.html#D7">NATTRA_1:def 7</a><br/>

<b>consider </b><font color="Maroon">t1</font> being    <a href="nattra_1.html#M2">natural_transformation</a> of <font color="Maroon">F1</font>,<font color="Maroon">G1</font>, <font color="Maroon">t2</font> being    <a href="nattra_1.html#M2">natural_transformation</a> of <font color="Maroon">F2</font>,<font color="Maroon">G2</font>;<br/>
<b>take </b>
<span class="p1"><a href="isocat_2.html#K15" target="_self">&lt;:</a><span class="default"><font color="Maroon">t1</font>,<font color="Maroon">t2</font></span><a href="isocat_2.html#K15" target="_self">:&gt;</a></span>
;<br/>

<b>thus </b><a NAME="E6:57"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1">Element</a> of the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">A</font>  holds <br/>(  <a href="cat_1.html#K6">Hom</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or for <font color="Olive">b<sub>3</sub></font> being   <a href="cat_1.html#M1">Morphism</a> of <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> holds  <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K15" target="_self">&lt;:</a><span class="default"><font color="Maroon">t1</font>,<font color="Maroon">t2</font></span><a href="isocat_2.html#K15" target="_self">:&gt;</a></span> <a href="nattra_1.html#K5">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">F1</font>,<font color="Maroon">F2</font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <a href="nattra_1.html#K3">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">G1</font>,<font color="Maroon">G2</font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <a href="nattra_1.html#K3">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K15" target="_self">&lt;:</a><span class="default"><font color="Maroon">t1</font>,<font color="Maroon">t2</font></span><a href="isocat_2.html#K15" target="_self">:&gt;</a></span> <a href="nattra_1.html#K5">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> )
 <b>by </b><i>, , </i>;<br/>


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