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<b>let </b><font color="Maroon">C</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">G1</font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">B</font>,<font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">G2</font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">B</font>,<font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">t</font> be    <a href="nattra_1.html#M2">natural_transformation</a> of <font color="Maroon">G1</font>,<font color="Maroon">G2</font>;<br/>









<b>assume </b><a NAME="E1:43"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">G1</font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Maroon">G2</font>
 ;<br/>

<a NAME="E2:43"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">G1</font> <a href="cat_1.html#K14">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K15">id</a> <font color="Maroon">B</font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">G1</font> &amp; <font color="Maroon">G2</font> <a href="cat_1.html#K14">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K15">id</a> <font color="Maroon">B</font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">G2</font> )
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">s</font> = <font color="Maroon">t</font> <a href="isocat_1.html#K5" target="_self">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K15">id</a> <font color="Maroon">B</font></span>)</span> as    <a href="nattra_1.html#M2">natural_transformation</a> of <font color="Maroon">G1</font>,<font color="Maroon">G2</font> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">b</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">B</font>;<br/><b>thus </b><font color="Maroon">s</font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">b</font> = 
<font color="Maroon">t</font> <a href="nattra_1.html#K5">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K15">id</a> <font color="Maroon">B</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i><a class="ref" href="isocat_1.html#T7" target="_self">Th7</a>, , </i>
<br/>.= 
<font color="Maroon">t</font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="cat_1.html#T118">CAT_1:118</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:43"/>
<font color="Maroon">t</font> <a href="isocat_1.html#K5" target="_self">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K15">id</a> <font color="Maroon">B</font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">t</font>
 <b>by </b><i><a class="ref" href="isocat_1.html#T7" target="_self">Th7</a>, </i>;<br/>


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