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

<b>let </b><font color="Maroon">B</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">F</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">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><b>that </b><br/><a NAME="E1:34"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">F</font> <a href="nattra_1.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">F1</font>
 <b>and </b><br/><a NAME="E2:34"/><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>
 ;<br/>

<b>let </b><font color="Maroon">t1</font> be    <a href="nattra_1.html#M1" target="_self">transformation</a> of <font color="Maroon">F</font>,<font color="Maroon">F1</font>;<br/>

<b>assume </b><a NAME="E3:34"/><i><font color="Green">E25</font></i>: 
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"><font color="Maroon">t1</font> <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">F</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"><font color="Maroon">t1</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Olive">a</font></span>)</span>
 ;<br/>

<b>let </b><font color="Maroon">t2</font> be    <a href="nattra_1.html#M1" target="_self">transformation</a> of <font color="Maroon">F1</font>,<font color="Maroon">F2</font>;<br/>

<b>assume </b><a NAME="E4:34"/><i><font color="Green">E26</font></i>: 
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"><font color="Maroon">t2</font> <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">F1</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">F2</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"><font color="Maroon">t2</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Olive">a</font></span>)</span>
 ;<br/>

<b>let </b><font color="Maroon">a</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font>, <font color="Maroon">b</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font>;<br/>

<b>assume </b><a NAME="E5:34"/><i><font color="Green">E27</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E6:34"/><b>then </b><i><font color="Green">E33</font></i>: 
(  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F1</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</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>, <a class="ref" href="cat_1.html#T126">CAT_1:126</a></i>;<br/>
<a NAME="E7:34"/><i><font color="Green">E34</font></i>: 
(  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font></span>)</span>,<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> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <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="E8:34"/><i><font color="Green">E35</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">b</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</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="E9:34"/><i><font color="Green">E36</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <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>,<span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</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="cat_1.html#T126">CAT_1:126</a></i>;<br/>
<a NAME="E10:34"/><i><font color="Green">E37</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">F1</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</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="cat_1.html#T126">CAT_1:126</a></i>;<br/>
<b>let </b><font color="Maroon">f</font> be    <a href="cat_1.html#M1">Morphism</a> of <font color="Maroon">a</font>,<font color="Maroon">b</font>;<br/>

<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t2</font> <a href="nattra_1.html#K6" target="_self">`*`</a> <font color="Maroon">t1</font></span>)</span> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">b</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Maroon">f</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t2</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">b</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">t1</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Maroon">f</font></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">t2</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">b</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#K5" target="_self">.</a> <font color="Maroon">b</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Maroon">f</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="nattra_1.html#E6:34"><i><font color="Green">E33</font></i></a>, <a class="txt" href="nattra_1.html#E8:34"><i><font color="Green">E35</font></i></a>, <a class="ref" href="cat_1.html#T54">CAT_1:54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">t2</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">b</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">F1</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Maroon">f</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">t1</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">a</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t2</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">b</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">F1</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">t1</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i><a class="txt" href="nattra_1.html#E7:34"><i><font color="Green">E34</font></i></a>, <a class="txt" href="nattra_1.html#E8:34"><i><font color="Green">E35</font></i></a>, <a class="txt" href="nattra_1.html#E10:34"><i><font color="Green">E37</font></i></a>, <a class="ref" href="cat_1.html#T54">CAT_1:54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F2</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Maroon">f</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">t2</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">t1</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Maroon">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">t2</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">a</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">t1</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">a</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="nattra_1.html#E7:34"><i><font color="Green">E34</font></i></a>, <a class="txt" href="nattra_1.html#E9:34"><i><font color="Green">E36</font></i></a>, <a class="ref" href="cat_1.html#T54">CAT_1:54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Maroon">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">t2</font> <a href="nattra_1.html#K6" target="_self">`*`</a> <font color="Maroon">t1</font></span>)</span> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i>, , </i>
;<br/>


</div>
