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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>) <b>-&gt; </b>   <a href="cat_1.html#M1">Morphism</a> of <font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">a<sub>1</sub></font> =  <a href="cat_1.html#K10">id</a> <font color="Maroon">a<sub>1</sub></font>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>] <b>means </b>verum;<br/>
<b>defpred </b><font color="Maroon">S<sub>2</sub></font>[  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>] <b>means </b><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">a<sub>1</sub></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>set </b><font color="Maroon">M</font> = <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">a</font>) where <font color="Olive">a</font> is   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">a</font>] </span>}</span> ;<br/>
<b>set </b><font color="Maroon">N</font> = <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">a</font>) where <font color="Olive">a</font> is   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font> : <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">a</font>] </span>}</span> ;<br/>
<a NAME="E1:75_1_1"/><i><font color="Green">E7</font></i>: 
for <font color="Olive">a</font> being  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font> holds <br/> ( <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">a</font>] iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">a</font>] )
 
;<br/>
<a NAME="E2:75_1_1"/><i><font color="Green">E8</font></i>: 
<span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">a</font>) where <font color="Olive">a</font> is   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font> : <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">a</font>] </span>}</span>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">a</font>) where <font color="Olive">a</font> is   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">a</font>] </span>}</span> 
 
<b>from </b><i><a class="ref" href="fraenkel.html#S3">FRAENKEL:sch 3</a>();<br/></i>
<b>set </b><font color="Maroon">N'</font> = <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">a</font>) where <font color="Olive">a</font> is   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font> : ( <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">a</font>) <a href="hidden.html#R2">in</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">a</font>] ) </span>}</span> ;<br/>
<a NAME="E3:75_1_1"/><i><font color="Green">E25</font></i>: 
<span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">a</font>) where <font color="Olive">a</font> is   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font> : ( <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">a</font>) <a href="hidden.html#R2">in</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">a</font>] ) </span>}</span>  <a href="tarski.html#R1">c=</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font>
 
<b>from </b><i><a class="ref" href="fraenkel.html#S17">FRAENKEL:sch 17</a>();<br/></i>
<b>defpred </b><font color="Maroon">S<sub>3</sub></font>[  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>] <b>means </b>( <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">a<sub>1</sub></font>) <a href="hidden.html#R2">in</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">a<sub>1</sub></font>] );<br/>
<b>set </b><font color="Maroon">N''</font> = <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">a</font>) where <font color="Olive">a</font> is   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font> : <font color="Maroon">S<sub>3</sub></font>[<font color="Olive">a</font>] </span>}</span> ;<br/>
<a NAME="E4:75_1_1"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">a</font> being  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font> holds <br/> ( <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">a</font>] iff <font color="Maroon">S<sub>3</sub></font>[<font color="Olive">a</font>] )
 
;<br/>
<a NAME="E5:75_1_1"/><i><font color="Green">E27</font></i>: 
<span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">a</font>) where <font color="Olive">a</font> is   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font> : <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">a</font>] </span>}</span>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">a</font>) where <font color="Olive">a</font> is   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font> : <font color="Maroon">S<sub>3</sub></font>[<font color="Olive">a</font>] </span>}</span> 
 
<b>from </b><i><a class="ref" href="fraenkel.html#S3">FRAENKEL:sch 3</a>();<br/></i>
<b>consider </b><font color="Maroon">a</font> being   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>;<br/>
<a NAME="E7:75_1_1"/>
 <a href="cat_1.html#K10">id</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">a</font>) where <font color="Olive">a</font> is   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">a</font>] </span>}</span> 
 
;<br/>
<b>then reconsider </b><font color="Maroon">M</font> = <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">a</font>) where <font color="Olive">a</font> is   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">a</font>] </span>}</span>  as  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font> <b>by </b><i>, , </i>;<br/>
<a NAME="E9:75_1_1"/><i><font color="Green">E33</font></i>: 
the <a href="cat_1.html#U5">Comp</a> of <font color="Maroon">C</font> <a href="realset1.html#K1">||</a> <font color="Maroon">M</font> is   <a href="partfun1.html#NM1">PartFunc</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">M</font>,<font color="Maroon">M</font></span><a href="zfmisc_1.html#K2">:]</a></span>,the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="partfun1.html#T43">PARTFUN1:43</a></i>;<br/>
<a NAME="E10:75_1_1"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default">the <a href="cat_1.html#U5">Comp</a> of <font color="Maroon">C</font> <a href="realset1.html#K1">||</a> <font color="Maroon">M</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">M</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:75_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default">the <a href="cat_1.html#U5">Comp</a> of <font color="Maroon">C</font> <a href="realset1.html#K1">||</a> <font color="Maroon">M</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:75_1_1_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default">the <a href="cat_1.html#U5">Comp</a> of <font color="Maroon">C</font> <a href="realset1.html#K1">||</a> <font color="Maroon">M</font></span>)</span>
 <b>and </b><br/><a NAME="E4:75_1_1_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">the <a href="cat_1.html#U5">Comp</a> of <font color="Maroon">C</font> <a href="realset1.html#K1">||</a> <font color="Maroon">M</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E5:75_1_1_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> the <a href="cat_1.html#U5">Comp</a> of <font color="Maroon">C</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1"><a href="mcart_1.html#K12">[:</a><span class="default"><font color="Maroon">M</font>,<font color="Maroon">M</font></span><a href="mcart_1.html#K12">:]</a></span>
 
<b>by </b><i>, <a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/>
<a NAME="E6:75_1_1_1"/><b>then </b>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="mcart_1.html#K12">[:</a><span class="default"><font color="Maroon">M</font>,<font color="Maroon">M</font></span><a href="mcart_1.html#K12">:]</a></span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>then consider </b><font color="Maroon">y1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">y2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E8:75_1_1_1"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> &amp; <font color="Maroon">y2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> )
 <b>and </b><br/><a NAME="E9:75_1_1_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y1</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T103">ZFMISC_1:103</a></i>;<br/>
<b>consider </b><font color="Maroon">a1</font> being   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font><b> such that </b><br/><a NAME="E11:75_1_1_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">y1</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10">id</a> <font color="Maroon">a1</font>
 <b>by </b><i><a class="ref" href="nattra_1.html#T5" target="_self">Th5</a></i>;<br/>
<b>consider </b><font color="Maroon">a2</font> being   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font><b> such that </b><br/><a NAME="E13:75_1_1_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">y2</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10">id</a> <font color="Maroon">a2</font>
 <b>by </b><i><a class="ref" href="nattra_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E14:75_1_1_1"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> the <a href="cat_1.html#U5">Comp</a> of <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="nattra_1.html#T4" target="_self">Th4</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E15:75_1_1_1"/><i><font color="Green">E42</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <font color="Maroon">a1</font>,<font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="cat_1.html#T56">CAT_1:56</a></i>;<br/>
<i><font color="Green">E43</font></i>: <font color="Maroon">a1</font> = 
 <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">a1</font></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#K3">cod</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a2</font></span>)</span>
<b>by </b><i><a class="ref" href="nattra_1.html#T6" target="_self">Th6</a>, , , , <a class="ref" href="cat_1.html#T40">CAT_1:40</a></i>
<br/>.= 
<font color="Maroon">a2</font>
<b>by </b><i><a class="ref" href="cat_1.html#T44">CAT_1:44</a></i>
;<br/>
 <a href="cat_1.html#K10">id</a> <font color="Maroon">a1</font> = 
<span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a1</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a1</font></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T59">CAT_1:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a1</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a2</font></span>)</span>
<b>by </b><i><a class="ref" href="nattra_1.html#T7" target="_self">Th7</a>, , <a class="ref" href="cat_1.html#D13">CAT_1:def 13</a></i>
<br/>.= 
the <a href="cat_1.html#U5">Comp</a> of <font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a1</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a2</font></span>)</span></span><a href="cat_2.html#K13">]</a></span>
<b>by </b><i><a class="ref" href="nattra_1.html#T6" target="_self">Th6</a>, , , , <a class="ref" href="cat_1.html#D4">CAT_1:def 4</a></i>
<br/>.= 
<font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="nattra_1.html#T4" target="_self">Th4</a>, <a class="ref" href="nattra_1.html#T6" target="_self">Th6</a>, , , <a class="ref" href="funct_1.html#T71">FUNCT_1:71</a></i>
;<br/>
<b>hence </b><a NAME="E18:75_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font>
 ;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">COMP</font> = the <a href="cat_1.html#U5">Comp</a> of <font color="Maroon">C</font> <a href="realset1.html#K1">||</a> <font color="Maroon">M</font> as   <a href="partfun1.html#NM1">PartFunc</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">M</font>,<font color="Maroon">M</font></span><a href="zfmisc_1.html#K2">:]</a></span>,<font color="Maroon">M</font> <b>by </b><i><a class="ref" href="nattra_1.html#T3" target="_self">Th3</a>, <a class="ref" href="partfun1.html#T29">PARTFUN1:29</a></i>;<br/>
<a NAME="E12:75_1_1"/><i><font color="Green">E44</font></i>: 
 <a href="relat_1.html#K1">dom</a> the <a href="cat_1.html#U6">Id</a> of <font color="Maroon">C</font> <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/>
<a NAME="E13:75_1_1"/>
 <a href="relat_1.html#K2">rng</a> the <a href="cat_1.html#U6">Id</a> of <font color="Maroon">C</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">M</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:75_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> the <a href="cat_1.html#U6">Id</a> of <font color="Maroon">C</font>
 ;<br/>

<b>then consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:75_1_1_2"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> the <a href="cat_1.html#U6">Id</a> of <font color="Maroon">C</font>
 <b>and </b><br/><a NAME="E4:75_1_1_2"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U6">Id</a> of <font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon">y</font> = <font color="Maroon">y</font> as   <a href="cat_1.html#NM1">Object</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/>
<a NAME="E6:75_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10">id</a> <font color="Maroon">y</font>
 
<b>by </b><i><a class="ref" href="nattra_1.html#T4" target="_self">Th4</a></i>;<br/>
<b>hence </b><a NAME="E7:75_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font>
 ;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">ID</font> = the <a href="cat_1.html#U6">Id</a> of <font color="Maroon">C</font> as   <a href="funct_2.html#NM1">Function</a> of the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C</font>,<font color="Maroon">M</font> <b>by </b><i>, <a class="ref" href="funct_2.html#T4">FUNCT_2:4</a></i>;<br/>
<a NAME="E15:75_1_1"/>
 <a href="relat_1.html#K1">dom</a> the <a href="cat_1.html#U6">Id</a> of <font color="Maroon">C</font> <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/>
<a NAME="E16:75_1_1"/><b>then </b><i><font color="Green">E47</font></i>: 
the <a href="cat_1.html#U6">Id</a> of <font color="Maroon">C</font> <a href="relat_1.html#K7">|</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U6">Id</a> of <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T97">RELAT_1:97</a></i>;<br/>
<a NAME="E17:75_1_1"/>
the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C</font> <a href="tarski.html#R1">c=</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> =  <a href="cat_1.html#G1">CatStr</a>(# the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C</font>,<font color="Maroon">M</font>,<span class="p1">(<span class="default">the <a href="cat_1.html#U3">Dom</a> of <font color="Maroon">C</font> <a href="nattra_1.html#K1" target="_self">|</a> <font color="Maroon">M</font></span>)</span>,<span class="p1">(<span class="default">the <a href="cat_1.html#U4">Cod</a> of <font color="Maroon">C</font> <a href="nattra_1.html#K1" target="_self">|</a> <font color="Maroon">M</font></span>)</span>,<font color="Maroon">COMP</font>,<font color="Maroon">ID</font> #) as    <a href="cat_2.html#M3">Subcategory</a> of <font color="Maroon">C</font> <b>by </b><i>, </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1_1_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">f</font> be   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">A</font>;<br/><a NAME="E1:75_1_1_3"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font>
 ;<br/><b>then consider </b><font color="Maroon">a</font> being   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font><b> such that </b><br/><a NAME="E3:75_1_1_3"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10">id</a> <font color="Maroon">a</font>
 ;<br/><b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">a</font> as   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font> ;<br/><b>take </b><font color="Maroon">a</font> = <font color="Maroon">a</font>;<br/><b>thus </b><a NAME="E5:75_1_1_3"/>
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10">id</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="nattra_1.html#T4" target="_self">Th4</a></i>;<br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">A</font> = <font color="Maroon">A</font> as  <a href="cat_1.html#V1">strict</a> <a href="nattra_1.html#V2" target="_self">discrete</a>  <a href="cat_2.html#M3">Subcategory</a> of <font color="Maroon">C</font> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">A</font>
;<br/>

<b>thus </b><a NAME="E21:75_1_1"/>
( the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C</font> &amp; the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Olive">a</font></span>)</span> where <font color="Olive">a</font> is   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font> : verum </span>}</span>  )
 ;<br/>


</div>
