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<b>let </b><font color="Maroon">A</font> be   <a href="altcat_1.html#NM4">category</a>;<br/><b>let </b><font color="Maroon">B</font> be   <a href="altcat_1.html#NM4">category</a>;<br/><b>let </b><font color="Maroon">C</font> be   <a href="altcat_1.html#NM4">category</a>;<br/><b>let </b><font color="Maroon">D</font> be   <a href="altcat_1.html#NM4">category</a>;<br/><b>let </b><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>;<br/><b>let </b><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>;<br/><b>let </b><font color="Maroon">G1</font> be  <a href="functor0.html#V15">covariant</a>  <a href="functor0.html#M2">Functor</a> of <font color="Maroon">B</font>,<font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">G2</font> be  <a href="functor0.html#V15">covariant</a>  <a href="functor0.html#M2">Functor</a> of <font color="Maroon">B</font>,<font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">H1</font> be  <a href="functor0.html#V15">covariant</a>  <a href="functor0.html#M2">Functor</a> of <font color="Maroon">C</font>,<font color="Maroon">D</font>, <font color="Maroon">H2</font> be  <a href="functor0.html#V15">covariant</a>  <a href="functor0.html#M2">Functor</a> of <font color="Maroon">C</font>,<font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">t</font> be    <a href="functor2.html#M1">transformation</a> of <font color="Maroon">F1</font>,<font color="Maroon">F2</font>;<br/><b>let </b><font color="Maroon">s</font> be    <a href="functor2.html#M1">transformation</a> of <font color="Maroon">G1</font>,<font color="Maroon">G2</font>;<br/><b>let </b><font color="Maroon">u</font> be    <a href="functor2.html#M1">transformation</a> of <font color="Maroon">H1</font>,<font color="Maroon">H2</font>;<br/>























<b>assume </b><a NAME="E1:43"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">F1</font> <a href="functor2.html#R1">is_transformable_to</a> <font color="Maroon">F2</font> &amp; <font color="Maroon">G1</font> <a href="functor2.html#R1">is_transformable_to</a> <font color="Maroon">G2</font> &amp; <font color="Maroon">H1</font> <a href="functor2.html#R1">is_transformable_to</a> <font color="Maroon">H2</font> )
 ;<br/>

<a NAME="E2:43"/><b>then </b><i><font color="Green">E32</font></i>: 
( <font color="Maroon">H1</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">G2</font> <a href="functor2.html#R1">is_transformable_to</a> <font color="Maroon">H2</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">G2</font> &amp; <font color="Maroon">H1</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">G1</font> <a href="functor2.html#R1">is_transformable_to</a> <font color="Maroon">H1</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">G2</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E3:43"/><b>then </b><i><font color="Green">E33</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">G2</font></span>)</span> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">F2</font> <a href="functor2.html#R1">is_transformable_to</a> <span class="p1">(<span class="default"><font color="Maroon">H2</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">G2</font></span>)</span> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">F2</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">G1</font></span>)</span> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">F2</font> <a href="functor2.html#R1">is_transformable_to</a> <span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">G2</font></span>)</span> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">F2</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">G1</font></span>)</span> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">F1</font> <a href="functor2.html#R1">is_transformable_to</a> <span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">G1</font></span>)</span> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">F2</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:43"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">G1</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">F2</font> <a href="functor2.html#R1">is_transformable_to</a> <font color="Maroon">G2</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">F2</font> &amp; <font color="Maroon">G1</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">F1</font> <a href="functor2.html#R1">is_transformable_to</a> <font color="Maroon">G1</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">F2</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:43"/><i><font color="Green">E35</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="functor3.html#K6" target="_self">*</a> <font color="Maroon">G2</font></span>)</span> <a href="functor3.html#K6" target="_self">*</a> <font color="Maroon">F2</font> <a href="pboole.html#R6">=</a> <font color="Maroon">u</font> <a href="functor3.html#K6" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">G2</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">F2</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="functor3.html#K5" target="_self">*</a> <font color="Maroon">s</font></span>)</span> <a href="functor3.html#K6" target="_self">*</a> <font color="Maroon">F2</font> <a href="pboole.html#R6">=</a> <font color="Maroon">H1</font> <a href="functor3.html#K5" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="functor3.html#K6" target="_self">*</a> <font color="Maroon">F2</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">G1</font></span>)</span> <a href="functor3.html#K5" target="_self">*</a> <font color="Maroon">t</font> <a href="pboole.html#R6">=</a> <font color="Maroon">H1</font> <a href="functor3.html#K5" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">G1</font> <a href="functor3.html#K5" target="_self">*</a> <font color="Maroon">t</font></span>)</span> )
 
<b>by </b><i>, , , </i>;<br/>
<a NAME="E6:43"/><i><font color="Green">E44</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">G1</font></span>)</span> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">F1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H1</font> <a href="functor3.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">G1</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">F1</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">G1</font></span>)</span> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">F2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H1</font> <a href="functor3.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">G1</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">F2</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">G2</font></span>)</span> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">F2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H1</font> <a href="functor3.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">G2</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">F2</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">H2</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">G2</font></span>)</span> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">F2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H2</font> <a href="functor3.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">G2</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">F2</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="functor0.html#T33">FUNCTOR0:33</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="functor3.html#K7" target="_self">(#)</a> <font color="Maroon">s</font></span>)</span> <a href="functor3.html#K7" target="_self">(#)</a> <font color="Maroon">t</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="functor3.html#K6" target="_self">*</a> <font color="Maroon">G2</font></span>)</span> <a href="functor3.html#K6" target="_self">*</a> <font color="Maroon">F2</font></span>)</span> <a href="functor2.html#K3">`*`</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">H1</font> <a href="functor3.html#K5" target="_self">*</a> <font color="Maroon">s</font></span>)</span> <a href="functor3.html#K6" target="_self">*</a> <font color="Maroon">F2</font></span>)</span></span>)</span> <a href="functor2.html#K3">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">H1</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">G1</font></span>)</span> <a href="functor3.html#K5" target="_self">*</a> <font color="Maroon">t</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="functor3.html#K6" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">G2</font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">F2</font></span>)</span></span>)</span> <a href="functor2.html#K3">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">H1</font> <a href="functor3.html#K5" target="_self">*</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="functor3.html#K6" target="_self">*</a> <font color="Maroon">F2</font></span>)</span></span>)</span> <a href="functor2.html#K3">`*`</a> <span class="p2">(<span class="default"><font color="Maroon">H1</font> <a href="functor3.html#K5" target="_self">*</a> <span class="p3">(<span class="default"><font color="Maroon">G1</font> <a href="functor3.html#K5" target="_self">*</a> <font color="Maroon">t</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, , , <a class="ref" href="functor2.html#T8">FUNCTOR2:8</a></i>
<br/>.= 
<font color="Maroon">u</font> <a href="functor3.html#K7" target="_self">(#)</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="functor3.html#K7" target="_self">(#)</a> <font color="Maroon">t</font></span>)</span>
<b>by </b><i>, </i>
;<br/>


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