<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="index_1.html#NM9">Indexing</a> of <font color="Maroon">c<sub>4</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>







<b>assume </b><a NAME="E1:63"/><i><font color="Green">E32</font></i>: 
(  <a href="cat_5.html#K7">Image</a> <font color="Maroon">c<sub>6</sub></font> is    <a href="cat_2.html#M3">Subcategory</a> of <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="cat_5.html#K7">Image</a> <font color="Maroon">c<sub>7</sub></font> is    <a href="cat_2.html#M3">Subcategory</a> of <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>6</sub></font> as    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">c<sub>1</sub></font>, <a href="cat_5.html#K7">Image</a> <font color="Maroon">c<sub>6</sub></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">c<sub>9</sub></font> = <font color="Maroon">c<sub>7</sub></font> as    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">c<sub>1</sub></font>, <a href="cat_5.html#K7">Image</a> <font color="Maroon">c<sub>7</sub></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">c<sub>10</sub></font> = <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>9</sub></font> as    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> <b>by </b><i><a class="txt" href="index_1.html#E1:63"><i><font color="Green">E32</font></i></a>, <a class="txt" href="index_1.html#E42"><i><font color="Green">Lemma29</font></i></a></i>;<br/>
<a NAME="E5:63"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="index_1.html#K20" target="_self">*</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p3">(<span class="default"><a href="index_1.html#K16" target="_self">rng</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="cat_1.html#K14">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="index_1.html#K19" target="_self">-indexing_of</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="index_1.html#K20" target="_self">*</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p3">(<span class="default"><a href="index_1.html#K16" target="_self">rng</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="cat_1.html#K14">*</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="index_1.html#K19" target="_self">-indexing_of</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="index_1.html#E1:63"><i><font color="Green">E32</font></i></a>, <a class="ref" href="index_1.html#D16" target="_self">Def16</a></i>;<br/>
<b>hence </b><a NAME="E6:63"/>
<font color="Maroon">c<sub>5</sub></font> <a href="index_1.html#K20" target="_self">*</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="index_1.html#K20" target="_self">*</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="index_1.html#E1:63"><i><font color="Green">E32</font></i></a></i>;<br/>


</div>
