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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">C</font> be   <a href="cat_1.html#NM4">Category</a>;<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>, <font color="Maroon">G1</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">C</font>, <font color="Maroon">G2</font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">C</font>;<br/>









<b>assume </b><a NAME="E1:52"/><i><font color="Green">E16</font></i>: 
( <font color="Maroon">F1</font> <a href="nattra_1.html#R1">is_transformable_to</a> <font color="Maroon">G1</font> &amp; <font color="Maroon">F2</font> <a href="nattra_1.html#R1">is_transformable_to</a> <font color="Maroon">G2</font> )
 ;<br/>

<b>let </b><font color="Maroon">t1</font> be    <a href="nattra_1.html#M1">transformation</a> of <font color="Maroon">F1</font>,<font color="Maroon">G1</font>;<br/><b>let </b><font color="Maroon">t2</font> be    <a href="nattra_1.html#M1">transformation</a> of <font color="Maroon">F2</font>,<font color="Maroon">G2</font>;<br/><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="E2:52"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">t1</font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <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">G1</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font></span>)</span> &amp; <font color="Maroon">t2</font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <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">G2</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font></span>)</span> )
 
<b>by </b><i>, <a class="ref" href="isocat_1.html#T7">ISOCAT_1:7</a></i>;<br/>
<a NAME="E3:52"/>
( <span class="p1"><a href="cat_2.html#K12">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">F1</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F2</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font></span>)</span></span><a href="cat_2.html#K12">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">F1</font>,<font color="Maroon">F2</font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font> &amp; <span class="p1"><a href="cat_2.html#K12">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">G1</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">G2</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font></span>)</span></span><a href="cat_2.html#K12">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">G1</font>,<font color="Maroon">G2</font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font> &amp; <span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">t1</font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">t2</font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">a</font></span>)</span></span><a href="cat_2.html#K13">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="funct_3.html#K14">&lt;:</a><span class="default"><font color="Maroon">t1</font>,<font color="Maroon">t2</font></span><a href="funct_3.html#K14">:&gt;</a></span> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> )
 
<b>by </b><i>, <a class="ref" href="isocat_2.html#T9" target="_self">Th9</a>, <a class="ref" href="isocat_2.html#D1" target="_self">Def1</a></i>;<br/>
<b>hence </b><a NAME="E4:52"/>
<span class="p1"><a href="funct_3.html#K14">&lt;:</a><span class="default"><font color="Maroon">t1</font>,<font color="Maroon">t2</font></span><a href="funct_3.html#K14">:&gt;</a></span> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">F1</font>,<font color="Maroon">F2</font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">G1</font>,<font color="Maroon">G2</font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font></span>)</span>
 <b>by </b><i>, <a class="txt" href="isocat_2.html#E1:52"><i><font color="Green">E16</font></i></a></i>;<br/>


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