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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">T</font> be    <a href="index_1.html#M4" target="_self">TargetCat</a> of <font color="Maroon">I</font>;<br/>





<a NAME="E1:45"/><i><font color="Green">E23</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">T</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"><font color="Maroon">I</font> <a href="index_1.html#K10" target="_self">`1</a> </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>, <a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_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="E1:45_1"/>
<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/><a NAME="E3:45_1"/><i><font color="Green">E26</font></i>: 
(  <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp;  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 <b>by </b><i><a class="ref" href="cat_1.html#T44">CAT_1:44</a></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">T</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> = 
 <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K12">Obj</a> <span class="p4">(<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">T</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T44">CAT_1:44</a></i>
<br/>.= 
 <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><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">T</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T104">CAT_1:104</a></i>
<br/>.= 
<span class="p1">(<span class="default"><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">T</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="mcart_1.html#K17">`11</a> 
<b>by </b><i><a class="ref" href="cat_5.html#T2">CAT_5:2</a></i>
<br/>.= 
<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> <font color="Maroon">a</font></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> <font color="Maroon">a</font></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> <span class="p3">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a</font></span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="mcart_1.html#K17">`11</a> 
<b>by </b><i>, </i>
;<br/><b>hence </b><a NAME="E5:45_1"/>
<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">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <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="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="mcart_1.html#T89">MCART_1:89</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:45"/>
 <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">T</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">I</font> <a href="index_1.html#K10" target="_self">`1</a> 
 <b>by </b><i>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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