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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="cat_5.html#V3">Categorial</a> <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="index_1.html#NM9">Indexing</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="index_1.html#NM9">Indexing</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="index_1.html#M4" target="_self">TargetCat</a> of <font color="Maroon">c<sub>4</sub></font>;<br/>









<b>assume </b><a NAME="E1:76"/>
<font color="Maroon">c<sub>2</sub></font> is    <a href="index_1.html#M4" target="_self">TargetCat</a> of <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>2</sub></font> as    <a href="index_1.html#M4" target="_self">TargetCat</a> of <font color="Maroon">c<sub>3</sub></font> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="index_1.html#NM9">Indexing</a> of <font color="Maroon">c<sub>6</sub></font> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>5</sub></font> as    <a href="index_1.html#M4" target="_self">TargetCat</a> of <font color="Maroon">c<sub>7</sub></font> ;<br/>
<a NAME="E5:76"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="index_1.html#K16" target="_self">rng</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="index_1.html#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E6:76"/><i><font color="Green">E41</font></i>: 
(  <a href="cat_5.html#K7">Image</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="index_1.html#K16" target="_self">rng</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="cat_5.html#K7">Image</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="index_1.html#K16" target="_self">rng</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="index_1.html#K16" target="_self">rng</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="index_1.html#D12" target="_self">Def12</a></i>;<br/>
<b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="index_1.html#K22" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font> = 
<font color="Maroon">c<sub>4</sub></font> <a href="index_1.html#K20" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="index_1.html#K16" target="_self">rng</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>

<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="index_1.html#K20" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="index_1.html#E5:76"><i><font color="Green">E40</font></i></a>, <a class="txt" href="index_1.html#E6:76"><i><font color="Green">E41</font></i></a>, <a class="ref" href="index_1.html#T22" target="_self">Th22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="cat_1.html#K14">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></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="ref" href="index_1.html#T23" target="_self">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="index_1.html#K21" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="index_1.html#D17" target="_self">Def17</a></i>
;<br/>


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