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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="nattra_1.html#M2">natural_transformation</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>









<b>assume </b><a NAME="E1:43"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E2:43"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>4</sub></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">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="ref" href="isocat_1.html#T4" target="_self">Th4</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></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">c<sub>2</sub></font></span>)</span> as    <a href="nattra_1.html#M2">natural_transformation</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></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">c<sub>7</sub></font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>thus </b><font color="Maroon">c<sub>6</sub></font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>5</sub></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">c<sub>2</sub></font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_1.html#E1:43"><i><font color="Green">E35</font></i></a>, <a class="txt" href="isocat_1.html#E2:43"><i><font color="Green">E36</font></i></a>, <a class="ref" href="isocat_1.html#T29" target="_self">Th29</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>7</sub></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">c<sub>5</sub></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">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="isocat_1.html#E1:43"><i><font color="Green">E35</font></i></a>, <a class="ref" href="isocat_1.html#T31" target="_self">Th31</a></i>;<br/>


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