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<b>let </b><font color="Maroon">IT1</font> be    <a href="cat_1.html#M2">Functor</a> of  <a href="nattra_1.html#K12">Functors</a> <font color="Maroon">A</font>,<span class="p1"><a href="cat_2.html#K11">[:</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="cat_2.html#K11">:]</a></span>,<span class="p1"><a href="cat_2.html#K11">[:</a><span class="default"><span class="p2">(<span class="default"><a href="nattra_1.html#K12">Functors</a> <font color="Maroon">A</font>,<font color="Maroon">B</font></span>)</span>,<span class="p2">(<span class="default"><a href="nattra_1.html#K12">Functors</a> <font color="Maroon">A</font>,<font color="Maroon">C</font></span>)</span></span><a href="cat_2.html#K11">:]</a></span>, <font color="Maroon">IT2</font> be    <a href="cat_1.html#M2">Functor</a> of  <a href="nattra_1.html#K12">Functors</a> <font color="Maroon">A</font>,<span class="p1"><a href="cat_2.html#K11">[:</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="cat_2.html#K11">:]</a></span>,<span class="p1"><a href="cat_2.html#K11">[:</a><span class="default"><span class="p2">(<span class="default"><a href="nattra_1.html#K12">Functors</a> <font color="Maroon">A</font>,<font color="Maroon">B</font></span>)</span>,<span class="p2">(<span class="default"><a href="nattra_1.html#K12">Functors</a> <font color="Maroon">A</font>,<font color="Maroon">C</font></span>)</span></span><a href="cat_2.html#K11">:]</a></span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:60_1_2"/><i><font color="Green">E82</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>,<span class="p1"><a href="cat_2.html#K11">[:</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="cat_2.html#K11">:]</a></span>  st <font color="Olive">F1</font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Olive">F2</font> holds <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> holds  <font color="Maroon">IT1</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> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4">(<span class="default"><a href="isocat_2.html#K11" target="_self">Pr1</a> <font color="Olive">F1</font></span>)</span>,<span class="p4">(<span class="default"><a href="isocat_2.html#K11" target="_self">Pr1</a> <font color="Olive">F2</font></span>)</span></span><a href="tarski.html#K4">]</a></span>,<span class="p3">(<span class="default"><a href="isocat_2.html#K13" target="_self">Pr1</a> <font color="Olive">t</font></span>)</span></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4">(<span class="default"><a href="isocat_2.html#K12" target="_self">Pr2</a> <font color="Olive">F1</font></span>)</span>,<span class="p4">(<span class="default"><a href="isocat_2.html#K12" target="_self">Pr2</a> <font color="Olive">F2</font></span>)</span></span><a href="tarski.html#K4">]</a></span>,<span class="p3">(<span class="default"><a href="isocat_2.html#K14" target="_self">Pr2</a> <font color="Olive">t</font></span>)</span></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K4">]</a></span>
 <b>and </b><br/><a NAME="E2:60_1_2"/><i><font color="Green">E83</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>,<span class="p1"><a href="cat_2.html#K11">[:</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="cat_2.html#K11">:]</a></span>  st <font color="Olive">F1</font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Olive">F2</font> holds <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> holds  <font color="Maroon">IT2</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> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4">(<span class="default"><a href="isocat_2.html#K11" target="_self">Pr1</a> <font color="Olive">F1</font></span>)</span>,<span class="p4">(<span class="default"><a href="isocat_2.html#K11" target="_self">Pr1</a> <font color="Olive">F2</font></span>)</span></span><a href="tarski.html#K4">]</a></span>,<span class="p3">(<span class="default"><a href="isocat_2.html#K13" target="_self">Pr1</a> <font color="Olive">t</font></span>)</span></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4">(<span class="default"><a href="isocat_2.html#K12" target="_self">Pr2</a> <font color="Olive">F1</font></span>)</span>,<span class="p4">(<span class="default"><a href="isocat_2.html#K12" target="_self">Pr2</a> <font color="Olive">F2</font></span>)</span></span><a href="tarski.html#K4">]</a></span>,<span class="p3">(<span class="default"><a href="isocat_2.html#K14" target="_self">Pr2</a> <font color="Olive">t</font></span>)</span></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K4">]</a></span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">f</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>,<span class="p2"><a href="cat_2.html#K11">[:</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="cat_2.html#K11">:]</a></span></span>)</span>;<br/><b>consider </b><font color="Maroon">F1</font> being    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">A</font>,<span class="p1"><a href="cat_2.html#K11">[:</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="cat_2.html#K11">:]</a></span>, <font color="Maroon">F2</font> being    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">A</font>,<span class="p1"><a href="cat_2.html#K11">[:</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="cat_2.html#K11">:]</a></span>, <font color="Maroon">s</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="E2:60_1_2_1"/><i><font color="Green">E92</font></i>: 
<font color="Maroon">F1</font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Maroon">F2</font>
 <b>and </b><br/><a NAME="E3:60_1_2_1"/><i><font color="Green">E93</font></i>: 
(  <a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F1</font> &amp;  <a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font> &amp; <font color="Maroon">f</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">s</font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i/>;<br/><b>thus </b><font color="Maroon">IT1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font> = 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4">(<span class="default"><a href="isocat_2.html#K11" target="_self">Pr1</a> <font color="Maroon">F1</font></span>)</span>,<span class="p4">(<span class="default"><a href="isocat_2.html#K11" target="_self">Pr1</a> <font color="Maroon">F2</font></span>)</span></span><a href="tarski.html#K4">]</a></span>,<span class="p3">(<span class="default"><a href="isocat_2.html#K13" target="_self">Pr1</a> <font color="Maroon">s</font></span>)</span></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4">(<span class="default"><a href="isocat_2.html#K12" target="_self">Pr2</a> <font color="Maroon">F1</font></span>)</span>,<span class="p4">(<span class="default"><a href="isocat_2.html#K12" target="_self">Pr2</a> <font color="Maroon">F2</font></span>)</span></span><a href="tarski.html#K4">]</a></span>,<span class="p3">(<span class="default"><a href="isocat_2.html#K14" target="_self">Pr2</a> <font color="Maroon">s</font></span>)</span></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i>, , </i>
<br/>.= 
<font color="Maroon">IT2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font>
<b>by </b><i>, , </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:60_1_2"/>
<font color="Maroon">IT1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">IT2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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