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<b>let </b><font color="Maroon">f1</font> be    <a href="cat_1.html#M2">Functor</a> of  <a href="nattra_1.html#K12">Functors</a> <font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">B</font>, <font color="Maroon">f2</font> be    <a href="cat_1.html#M2">Functor</a> of  <a href="nattra_1.html#K12">Functors</a> <font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">B</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:11_1_2"/><i><font color="Green">E80</font></i>: 
for <font color="Olive">F1</font>, <font color="Olive">F2</font> being   <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font><br/> for <font color="Olive">t</font> being   <a href="nattra_1.html#M2">natural_transformation</a> of <font color="Olive">F1</font>,<font color="Olive">F2</font>  st <font color="Olive">F1</font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Olive">F2</font> holds <br/><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">F1</font>,<font color="Olive">F2</font></span><a href="tarski.html#K4">]</a></span>,<font color="Olive">t</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <font color="Olive">t</font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">a</font>
 <b>and </b><br/><a NAME="E2:11_1_2"/><i><font color="Green">E81</font></i>: 
for <font color="Olive">F1</font>, <font color="Olive">F2</font> being   <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font><br/> for <font color="Olive">t</font> being   <a href="nattra_1.html#M2">natural_transformation</a> of <font color="Olive">F1</font>,<font color="Olive">F2</font>  st <font color="Olive">F1</font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Olive">F2</font> holds <br/><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">F1</font>,<font color="Olive">F2</font></span><a href="tarski.html#K4">]</a></span>,<font color="Olive">t</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <font color="Olive">t</font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">a</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be   <a href="cat_1.html#NM2">Morphism</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K12">Functors</a> <font color="Maroon">A</font>,<font color="Maroon">B</font></span>)</span>;<br/><a NAME="E1:11_1_2_1"/>
the <a href="cat_1.html#U2">Morphisms</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K12">Functors</a> <font color="Maroon">A</font>,<font color="Maroon">B</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="nattra_1.html#K11">NatTrans</a> <font color="Maroon">A</font>,<font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="nattra_1.html#D18">NATTRA_1:def 18</a></i>;<br/><b>then consider </b><font color="Maroon">F1</font> being    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>, <font color="Maroon">F2</font> being    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>, <font color="Maroon">t</font> being    <a href="nattra_1.html#M2">natural_transformation</a> of <font color="Maroon">F1</font>,<font color="Maroon">F2</font><b> such that </b><br/><a NAME="E3:11_1_2_1"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">F1</font>,<font color="Maroon">F2</font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">t</font></span><a href="tarski.html#K4">]</a></span>
 <b>and </b><br/><a NAME="E4:11_1_2_1"/><i><font color="Green">E83</font></i>: 
<font color="Maroon">F1</font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Maroon">F2</font>
 <b>by </b><i><a class="ref" href="nattra_1.html#D15">NATTRA_1:def 15</a></i>;<br/><b>thus </b><font color="Maroon">f1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font> = 
<font color="Maroon">t</font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , </i>
<br/>.= 
<font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font>
<b>by </b><i>, , </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:11_1_2"/>
<font color="Maroon">f1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">f2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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