<?xml version="1.0"?>
<div class="add">

<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">C</font> be   <a href="cat_1.html#NM4">Category</a>;<br/>





<b>given </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">G1</font> being    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">B</font>,<font color="Maroon">A</font><b> such that </b><a NAME="E1:58"/><i><font color="Green">E18</font></i>: 
( <font color="Maroon">G1</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">F1</font> <a href="nattra_1.html#NR4" target="_self">~=</a>  <a href="cat_1.html#K15">id</a> <font color="Maroon">A</font> &amp; <font color="Maroon">F1</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">G1</font> <a href="nattra_1.html#NR4" target="_self">~=</a>  <a href="cat_1.html#K15">id</a> <font color="Maroon">B</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="isocat_1.html#D10" target="_self">ISOCAT_1:def 10</a><br/>

<b>given </b><font color="Maroon">F2</font> being    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">B</font>,<font color="Maroon">C</font>, <font color="Maroon">G2</font> being    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">C</font>,<font color="Maroon">B</font><b> such that </b><a NAME="E2:58"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">G2</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">F2</font> <a href="nattra_1.html#NR4" target="_self">~=</a>  <a href="cat_1.html#K15">id</a> <font color="Maroon">B</font> &amp; <font color="Maroon">F2</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">G2</font> <a href="nattra_1.html#NR4" target="_self">~=</a>  <a href="cat_1.html#K15">id</a> <font color="Maroon">C</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="isocat_1.html#D10" target="_self">ISOCAT_1:def 10</a><br/>

<b>take </b>
<font color="Maroon">F2</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">F1</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="isocat_1.html#D10" target="_self">ISOCAT_1:def 10</a><br/>

<b>take </b>
<font color="Maroon">G1</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">G2</font>
;<br/>

<a NAME="E3:58"/>
( <span class="p1">(<span class="default"><font color="Maroon">G1</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">G2</font></span>)</span> <a href="cat_1.html#K14">*</a> <font color="Maroon">F2</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">G1</font> <a href="cat_1.html#K14">*</a> <span class="p1">(<span class="default"><font color="Maroon">G2</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">F2</font></span>)</span> &amp; <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> )
 
<b>by </b><i>, <a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>;<br/>
<a NAME="E4:58"/><b>then </b><i><font color="Green">E22</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">G1</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">G2</font></span>)</span> <a href="cat_1.html#K14">*</a> <font color="Maroon">F2</font> <a href="nattra_1.html#NR4" target="_self">~=</a> <font color="Maroon">G1</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:58"/>
<span class="p1">(<span class="default"><font color="Maroon">G1</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">G2</font></span>)</span> <a href="cat_1.html#K14">*</a> <span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">F1</font></span>)</span> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G1</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">G2</font></span>)</span> <a href="cat_1.html#K14">*</a> <font color="Maroon">F2</font></span>)</span> <a href="cat_1.html#K14">*</a> <font color="Maroon">F1</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>;<br/>
<a NAME="E6:58"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">G1</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">G2</font></span>)</span> <a href="cat_1.html#K14">*</a> <span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">F1</font></span>)</span> <a href="nattra_1.html#NR4" target="_self">~=</a> <font color="Maroon">G1</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">F1</font>
 
<b>by </b><i><a class="ref" href="isocat_1.html#T9" target="_self">Th9</a>, </i>;<br/>
<b>hence </b><a NAME="E7:58"/>
<span class="p1">(<span class="default"><font color="Maroon">G1</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">G2</font></span>)</span> <a href="cat_1.html#K14">*</a> <span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">F1</font></span>)</span> <a href="nattra_1.html#NR4" target="_self">~=</a>  <a href="cat_1.html#K15">id</a> <font color="Maroon">A</font>
 <b>by </b><i>, <a class="ref" href="nattra_1.html#T32">NATTRA_1:32</a></i>;<br/>

<a NAME="E8:58"/>
( <span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">F1</font></span>)</span> <a href="cat_1.html#K14">*</a> <font color="Maroon">G1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">F2</font> <a href="cat_1.html#K14">*</a> <span class="p1">(<span class="default"><font color="Maroon">F1</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">G1</font></span>)</span> &amp; <font color="Maroon">F2</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">F2</font> )
 
<b>by </b><i>, <a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>;<br/>
<a NAME="E9:58"/><b>then </b><i><font color="Green">E23</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">F1</font></span>)</span> <a href="cat_1.html#K14">*</a> <font color="Maroon">G1</font> <a href="nattra_1.html#NR4" target="_self">~=</a> <font color="Maroon">F2</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E10:58"/>
<span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">F1</font></span>)</span> <a href="cat_1.html#K14">*</a> <span class="p1">(<span class="default"><font color="Maroon">G1</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">G2</font></span>)</span> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F2</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">F1</font></span>)</span> <a href="cat_1.html#K14">*</a> <font color="Maroon">G1</font></span>)</span> <a href="cat_1.html#K14">*</a> <font color="Maroon">G2</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>;<br/>
<a NAME="E11:58"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">F1</font></span>)</span> <a href="cat_1.html#K14">*</a> <span class="p1">(<span class="default"><font color="Maroon">G1</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">G2</font></span>)</span> <a href="nattra_1.html#NR4" target="_self">~=</a> <font color="Maroon">F2</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">G2</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E12:58"/>
<span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">F1</font></span>)</span> <a href="cat_1.html#K14">*</a> <span class="p1">(<span class="default"><font color="Maroon">G1</font> <a href="cat_1.html#K14">*</a> <font color="Maroon">G2</font></span>)</span> <a href="nattra_1.html#NR4" target="_self">~=</a>  <a href="cat_1.html#K15">id</a> <font color="Maroon">C</font>
 <b>by </b><i>, <a class="ref" href="nattra_1.html#T32">NATTRA_1:32</a></i>;<br/>


</div>
