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<b>let </b><font color="Maroon">C</font> be   <a href="cat_1.html#NM4">Category</a>, <font color="Maroon">D1</font> be   <a href="cat_1.html#NM4">Category</a>, <font color="Maroon">D2</font> be   <a href="cat_1.html#NM4">Category</a>, <font color="Maroon">E</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">I</font> be   <a href="index_1.html#NM9">Indexing</a> of <font color="Maroon">E</font>;<br/><b>let </b><font color="Maroon">F</font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">C</font>,<font color="Maroon">D1</font>;<br/><b>let </b><font color="Maroon">G</font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">C</font>,<font color="Maroon">D2</font>;<br/>







<b>assume </b><a NAME="E1:63"/><i><font color="Green">E23</font></i>: 
(  <a href="cat_5.html#K7">Image</a> <font color="Maroon">F</font> is    <a href="cat_2.html#M3">Subcategory</a> of <font color="Maroon">E</font> &amp;  <a href="cat_5.html#K7">Image</a> <font color="Maroon">G</font> is    <a href="cat_2.html#M3">Subcategory</a> of <font color="Maroon">E</font> &amp; <font color="Maroon">F</font> <a href="funct_2.html#R1">=</a> <font color="Maroon">G</font> )
 ;<br/>

<b>reconsider </b><font color="Maroon">F'</font> = <font color="Maroon">F</font> as    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">C</font>, <a href="cat_5.html#K7">Image</a> <font color="Maroon">F</font> <b>by </b><i><a class="ref" href="cat_5.html#T8">CAT_5:8</a></i>;<br/>
<b>reconsider </b><font color="Maroon">G'</font> = <font color="Maroon">G</font> as    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">C</font>, <a href="cat_5.html#K7">Image</a> <font color="Maroon">G</font> <b>by </b><i><a class="ref" href="cat_5.html#T8">CAT_5:8</a></i>;<br/>
<b>reconsider </b><font color="Maroon">F'</font> = <font color="Maroon">F'</font>, <font color="Maroon">G'</font> = <font color="Maroon">G'</font> as    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">C</font>,<font color="Maroon">E</font> <b>by </b><i>, </i>;<br/>
<a NAME="E5:63"/>
( <font color="Maroon">I</font> <a href="index_1.html#K20" target="_self">*</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">E</font>,<span class="p3">(<span class="default"><a href="index_1.html#K16" target="_self">rng</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="cat_1.html#K14">*</a> <font color="Maroon">F'</font></span>)</span> <a href="index_1.html#K19" target="_self">-indexing_of</a> <font color="Maroon">C</font> &amp; <font color="Maroon">I</font> <a href="index_1.html#K20" target="_self">*</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">E</font>,<span class="p3">(<span class="default"><a href="index_1.html#K16" target="_self">rng</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="cat_1.html#K14">*</a> <font color="Maroon">G'</font></span>)</span> <a href="index_1.html#K19" target="_self">-indexing_of</a> <font color="Maroon">C</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:63"/>
<font color="Maroon">I</font> <a href="index_1.html#K20" target="_self">*</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">I</font> <a href="index_1.html#K20" target="_self">*</a> <font color="Maroon">G</font>
 <b>by </b><i/>;<br/>


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