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<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> =  <a href="cat_5.html#K7">Image</a> <font color="Maroon">c<sub>4</sub></font> as    <a href="cat_2.html#M3">Subcategory</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="txt" href="index_1.html#E1:62"><i><font color="Green">E30</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>4</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>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>8</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>,<font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="txt" href="index_1.html#E42"><i><font color="Green">Lemma29</font></i></a></i>;<br/>
<b>take </b>
<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>3</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>8</sub></font></span>)</span> <a href="index_1.html#K19" target="_self">-indexing_of</a> <font color="Maroon">c<sub>1</sub></font>
;<br/>

<b>thus </b><a NAME="E4:62_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <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> st <font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> holds <br/><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>3</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>8</sub></font></span>)</span> <a href="index_1.html#K19" target="_self">-indexing_of</a> <font color="Maroon">c<sub>1</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>3</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="Olive">b<sub>1</sub></font></span>)</span> <a href="index_1.html#K19" target="_self">-indexing_of</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>


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