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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>assume </b><a NAME="E1:51"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">F1</font> <a href="nattra_1.html#R2" target="_self">is_naturally_transformable_to</a> <font color="Maroon">F2</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="nattra_1.html#D11" target="_self">NATTRA_1:def 11</a><br/>

<b>given </b><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><a NAME="E2:51"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">t</font> is <a href="nattra_1.html#V1" target="_self">invertible</a>
 ;<br/>

<b>thus </b><a NAME="E3:51"/>
<font color="Maroon">F2</font> <a href="nattra_1.html#R2" target="_self">is_naturally_transformable_to</a> <font color="Maroon">F1</font>
 <b>by </b><i>, , </i>; <i><font color="Red">:: according to </font></i><a class="ref" href="nattra_1.html#D11" target="_self">NATTRA_1:def 11</a><br/>

<b>take </b>
<font color="Maroon">t</font> <a href="nattra_1.html#K10" target="_self">"</a> 
;<br/>

<b>let </b><font color="Maroon">a</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="nattra_1.html#D10" target="_self">NATTRA_1:def 10</a><br/>

<a NAME="E4:51"/>
<font color="Maroon">F1</font> <a href="nattra_1.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">F2</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:51"/><b>then </b><i><font color="Green">E25</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">F1</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="nattra_1.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E6:51"/>
( <font color="Maroon">t</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">a</font> is <a href="cat_1.html#V5">invertible</a> &amp; <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="nattra_1.html#K10" target="_self">"</a> </span>)</span> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">a</font></span>)</span> <a href="cat_1.html#K11">"</a>  )
 
<b>by </b><i>, , , </i>;<br/>
<b>hence </b><a NAME="E7:51"/>
<span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="nattra_1.html#K10" target="_self">"</a> </span>)</span> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">a</font> is <a href="cat_1.html#V5">invertible</a>
 <b>by </b><i>, <a class="ref" href="cat_1.html#T76">CAT_1:76</a></i>;<br/>


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