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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="index_1.html#NM9">Indexing</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="index_1.html#M4" target="_self">TargetCat</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<b>set </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>2</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>3</sub></font>;<br/>
<a NAME="E1:60"/><i><font color="Green">E29</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being   <a href="pboole.html#M1">ManySortedSet</a> of the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>2</sub></font> being   <a href="pboole.html#M1">ManySortedSet</a> of the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="index_1.html#K7" target="_self">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="index_1.html#K7" target="_self">]</a></span>
 
<b>by </b><i><a class="ref" href="index_1.html#D4" target="_self">Def4</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>2</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>3</sub></font></span>)</span> <a href="index_1.html#K19" target="_self">-indexing_of</a> <font color="Maroon">c<sub>1</sub></font> = 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K12">Obj</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</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>3</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="mcart_1.html#K16">pr2</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</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>3</sub></font></span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span>

<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="index_1.html#K10" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><a href="mcart_1.html#K16">pr2</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</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>3</sub></font></span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="index_1.html#E24"><i><font color="Green">Lemma19</font></i></a></i>
<br/>.= 
<span class="p1"><a href="index_1.html#K12" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="index_1.html#K10" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="index_1.html#K14" target="_self">`2</a> </span>)</span></span><a href="index_1.html#K12" target="_self">]</a></span>
<b>by </b><i><a class="ref" href="index_1.html#T20" target="_self">Th20</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="index_1.html#E1:60"><i><font color="Green">E29</font></i></a>, <a class="ref" href="mcart_1.html#T8">MCART_1:8</a></i>
;<br/>


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