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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>assume </b><a NAME="E1:48"/><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>
 ;<br/>

<a NAME="E2:48"/><b>then </b><i><font color="Green">E8</font></i>: 
<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/>;<br/>
<b>assume </b><a NAME="E3:48"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">t1</font> is <a href="nattra_1.html#V1" target="_self">invertible</a>
 ;<br/>

<b>hence </b><a NAME="E4:48"/>
<font color="Maroon">F2</font> <a href="nattra_1.html#R1" target="_self">is_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#D7" target="_self">NATTRA_1:def 7</a><br/>

<b>take </b>
<font color="Maroon">t1</font> <a href="nattra_1.html#K9" target="_self">"</a> 
;<br/>

<b>thus </b><a NAME="E5:48"/>
for <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font>  st  <a href="cat_1.html#K6">Hom</a> <font color="Olive">a</font>,<font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  holds <br/>for <font color="Olive">f</font> being   <a href="cat_1.html#M1">Morphism</a> of <font color="Olive">a</font>,<font color="Olive">b</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t1</font> <a href="nattra_1.html#K9" target="_self">"</a> </span>)</span> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Olive">b</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Olive">f</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">F1</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Olive">f</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t1</font> <a href="nattra_1.html#K9" target="_self">"</a> </span>)</span> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Olive">a</font></span>)</span>
 <b>by </b><i>, , </i>;<br/>


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