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<b>let </b><font color="Maroon">A</font> be   <a href="altcat_1.html#NM4">category</a>, <font color="Maroon">B</font> be   <a href="altcat_1.html#NM4">category</a>;<br/><b>let </b><font color="Maroon">F</font> be  <a href="functor0.html#V15">covariant</a>  <a href="functor0.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>, <font color="Maroon">F1</font> be  <a href="functor0.html#V15">covariant</a>  <a href="functor0.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>, <font color="Maroon">F2</font> be  <a href="functor0.html#V15">covariant</a>  <a href="functor0.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>, <font color="Maroon">F3</font> be  <a href="functor0.html#V15">covariant</a>  <a href="functor0.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>;<br/>



<b>assume </b><a NAME="E1:13"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">F</font> <a href="functor2.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">F1</font> &amp; <font color="Maroon">F1</font> <a href="functor2.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">F2</font> &amp; <font color="Maroon">F2</font> <a href="functor2.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="functor2.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="functor2.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="functor2.html#M1" target="_self">transformation</a> of <font color="Maroon">F2</font>,<font color="Maroon">F3</font>;<br/>





<a NAME="E2:13"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">F</font> <a href="functor2.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">F2</font> &amp; <font color="Maroon">F1</font> <a href="functor2.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">F3</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:13"/><b>then </b><i><font color="Green">E30</font></i>: 
<font color="Maroon">F</font> <a href="functor2.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">F3</font>
 
<b>by </b><i>, </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A</font>;<br/><a NAME="E1:13_1"/><i><font color="Green">E32</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K3">.</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F1</font> <a href="functor0.html#K3">.</a> <font color="Maroon">a</font></span>)</span></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">F1</font> <a href="functor0.html#K3">.</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F2</font> <a href="functor0.html#K3">.</a> <font color="Maroon">a</font></span>)</span></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">F2</font> <a href="functor0.html#K3">.</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F3</font> <a href="functor0.html#K3">.</a> <font color="Maroon">a</font></span>)</span></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i>, </i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t3</font> <a href="functor2.html#K3" target="_self">`*`</a> <font color="Maroon">t2</font></span>)</span> <a href="functor2.html#K3" target="_self">`*`</a> <font color="Maroon">t1</font></span>)</span> <a href="functor2.html#K2" 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="functor2.html#K3" target="_self">`*`</a> <font color="Maroon">t2</font></span>)</span> <a href="functor2.html#K2" target="_self">!</a> <font color="Maroon">a</font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">t1</font> <a href="functor2.html#K2" target="_self">!</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t3</font> <a href="functor2.html#K2" target="_self">!</a> <font color="Maroon">a</font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p2">(<span class="default"><font color="Maroon">t2</font> <a href="functor2.html#K2" target="_self">!</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">t1</font> <a href="functor2.html#K2" 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">t3</font> <a href="functor2.html#K2" target="_self">!</a> <font color="Maroon">a</font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t2</font> <a href="functor2.html#K2" target="_self">!</a> <font color="Maroon">a</font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p2">(<span class="default"><font color="Maroon">t1</font> <a href="functor2.html#K2" target="_self">!</a> <font color="Maroon">a</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="altcat_1.html#T25">ALTCAT_1:25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">t3</font> <a href="functor2.html#K2" target="_self">!</a> <font color="Maroon">a</font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t2</font> <a href="functor2.html#K3" target="_self">`*`</a> <font color="Maroon">t1</font></span>)</span> <a href="functor2.html#K2" 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">t3</font> <a href="functor2.html#K3" target="_self">`*`</a> <span class="p2">(<span class="default"><font color="Maroon">t2</font> <a href="functor2.html#K3" target="_self">`*`</a> <font color="Maroon">t1</font></span>)</span></span>)</span> <a href="functor2.html#K2" target="_self">!</a> <font color="Maroon">a</font>
<b>by </b><i>, , </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:13"/>
<span class="p1">(<span class="default"><font color="Maroon">t3</font> <a href="functor2.html#K3" target="_self">`*`</a> <font color="Maroon">t2</font></span>)</span> <a href="functor2.html#K3" target="_self">`*`</a> <font color="Maroon">t1</font> <a href="pboole.html#R6">=</a> <font color="Maroon">t3</font> <a href="functor2.html#K3" target="_self">`*`</a> <span class="p1">(<span class="default"><font color="Maroon">t2</font> <a href="functor2.html#K3" target="_self">`*`</a> <font color="Maroon">t1</font></span>)</span>
 <b>by </b><i>, </i>;<br/>


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