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<b>let </b><font color="Maroon">C</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">C</font>;<br/><b>let </b><font color="Maroon">T1</font> be    <a href="index_1.html#M4" target="_self">TargetCat</a> of <font color="Maroon">I</font>, <font color="Maroon">T2</font> be    <a href="index_1.html#M4" target="_self">TargetCat</a> of <font color="Maroon">I</font>;<br/>





<a NAME="E1:46"/><i><font color="Green">E23</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">C</font>,<font color="Maroon">T1</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">C</font>,<font color="Maroon">T2</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:46_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font>
 ;<br/><b>then reconsider </b><font color="Maroon">f</font> = <font color="Maroon">x</font> as   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">C</font> ;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">C</font>,<font color="Maroon">T1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K10" target="_self">`1</a> </span>)</span> <a href="index_1.html#K2" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K10" target="_self">`1</a> </span>)</span> <a href="index_1.html#K2" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font></span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K14" target="_self">`2</a> </span>)</span> <a href="index_1.html#K13" target="_self">.</a> <font color="Maroon">f</font></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">C</font>,<font color="Maroon">T2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:46"/>
<font color="Maroon">I</font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">C</font>,<font color="Maroon">T1</font> <a href="funct_2.html#R1">=</a> <font color="Maroon">I</font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">C</font>,<font color="Maroon">T2</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>

<a NAME="E4:46"/><i><font color="Green">E26</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K12">Obj</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">C</font>,<font color="Maroon">T1</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K12">Obj</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">C</font>,<font color="Maroon">T2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:46_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C</font>
 ;<br/><b>then reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font> as   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="cat_1.html#K12">Obj</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">C</font>,<font color="Maroon">T1</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K10" target="_self">`1</a> </span>)</span> <a href="index_1.html#K2" target="_self">.</a> <font color="Maroon">a</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="cat_1.html#K12">Obj</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">C</font>,<font color="Maroon">T2</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:46"/>
 <a href="cat_1.html#K12">Obj</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">C</font>,<font color="Maroon">T1</font></span>)</span> <a href="funct_2.html#R1">=</a>  <a href="cat_1.html#K12">Obj</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">C</font>,<font color="Maroon">T2</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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