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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">F1</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">B</font>;<br/><b>let </b><font color="Maroon">t1</font> be    <a href="nattra_1.html#M2" target="_self">natural_transformation</a> of <font color="Maroon">F1</font>,<font color="Maroon">F2</font>;<br/>









<b>thus </b><a NAME="E1:58"/>
( <font color="Maroon">F1</font> <a href="nattra_1.html#R2" target="_self">is_naturally_transformable_to</a> <font color="Maroon">F2</font> implies <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">t1</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="nattra_1.html#K11" target="_self">NatTrans</a> <font color="Maroon">A</font>,<font color="Maroon">B</font> )
 <b>by </b><i/>;<br/>

<b>assume </b><a NAME="E2:58"/>
<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">t1</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="nattra_1.html#K11" target="_self">NatTrans</a> <font color="Maroon">A</font>,<font color="Maroon">B</font>
 ;<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" target="_self">natural_transformation</a> of <font color="Maroon">F1'</font>,<font color="Maroon">F2'</font><b> such that </b><br/><a NAME="E4:58"/><i><font color="Green">E7</font></i>: 
( <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">t1</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"><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> &amp; <font color="Maroon">F1'</font> <a href="nattra_1.html#R2" target="_self">is_naturally_transformable_to</a> <font color="Maroon">F2'</font> )
 <b>by </b><i/>;<br/>
<a NAME="E5:58"/>
<span class="p1"><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> <a href="hidden.html#R1">=</a> <span class="p1"><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>
 
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/>
<a NAME="E6:58"/><b>then </b>
( <font color="Maroon">F1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">F1'</font> &amp; <font color="Maroon">F2</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">F2'</font> )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/>
<b>hence </b><a NAME="E7:58"/>
<font color="Maroon">F1</font> <a href="nattra_1.html#R2" target="_self">is_naturally_transformable_to</a> <font color="Maroon">F2</font>
 <b>by </b><i/>;<br/>


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