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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">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>let </b><font color="Maroon">F3</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><a NAME="E1:31"/><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> &amp; <font color="Maroon">F1</font> <a href="nattra_1.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">F2</font> &amp; <font color="Maroon">F2</font> <a href="nattra_1.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">F3</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>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>let </b><font color="Maroon">t3</font> be    <a href="nattra_1.html#M1" target="_self">transformation</a> of <font color="Maroon">F2</font>,<font color="Maroon">F3</font>;<br/>





<a NAME="E2:31"/><i><font color="Green">E8</font></i>: 
( <font color="Maroon">F</font> <a href="nattra_1.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">F2</font> &amp; <font color="Maroon">F1</font> <a href="nattra_1.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">F3</font> )
 
<b>by </b><i><a class="txt" href="nattra_1.html#E3:31"><i><font color="Green">E25</font></i></a>, </i>;<br/>
<a NAME="E3:31"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">F</font> <a href="nattra_1.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">F3</font>
 
<b>by </b><i><a class="txt" href="nattra_1.html#E3:31"><i><font color="Green">E25</font></i></a>, </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font>;<br/><a NAME="E1:31_1"/><i><font color="Green">E26</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>  &amp;  <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">F3</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="txt" href="nattra_1.html#E3:31"><i><font color="Green">E25</font></i></a>, <a class="ref" href="nattra_1.html#T1" target="_self">Th1</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t3</font> <a href="nattra_1.html#K6" target="_self">`*`</a> <font color="Maroon">t2</font></span>)</span> <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 class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t3</font> <a href="nattra_1.html#K6" target="_self">`*`</a> <font color="Maroon">t2</font></span>)</span> <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="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#E3:31"><i><font color="Green">E25</font></i></a>, <a class="txt" href="nattra_1.html#E1:31_1"><i><font color="Green">E26</font></i></a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t3</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">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><a class="txt" href="nattra_1.html#E3:31"><i><font color="Green">E25</font></i></a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">t3</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="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="ref" href="cat_1.html#T54">CAT_1:54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">t3</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="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><a class="txt" href="nattra_1.html#E3:31"><i><font color="Green">E25</font></i></a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">t3</font> <a href="nattra_1.html#K6" target="_self">`*`</a> <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></span>)</span> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="txt" href="nattra_1.html#E3:31"><i><font color="Green">E25</font></i></a>, <a class="txt" href="nattra_1.html#E1:31_1"><i><font color="Green">E26</font></i></a>, </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:31"/>
<span class="p1">(<span class="default"><font color="Maroon">t3</font> <a href="nattra_1.html#K6" target="_self">`*`</a> <font color="Maroon">t2</font></span>)</span> <a href="nattra_1.html#K6" target="_self">`*`</a> <font color="Maroon">t1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">t3</font> <a href="nattra_1.html#K6" target="_self">`*`</a> <span class="p1">(<span class="default"><font color="Maroon">t2</font> <a href="nattra_1.html#K6" target="_self">`*`</a> <font color="Maroon">t1</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="nattra_1.html#T2" target="_self">Th2</a></i>;<br/>


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