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<b>let </b><font color="Maroon">A</font> be  <a href="nattra_1.html#V2" target="_self">discrete</a> <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font>;<br/>



<a NAME="E1:66"/><i><font color="Green">E7</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">a</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/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">g</font> be    <a href="cat_1.html#M1">Morphism</a> of <font color="Maroon">a</font>,<font color="Maroon">a</font>;<br/><b>consider </b><font color="Maroon">a2</font> being   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font><b> such that </b><br/><a NAME="E2:66_1"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10">id</a> <font color="Maroon">a2</font>
 <b>by </b><i/>;<br/><font color="Maroon">a</font> = 
 <a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font>
<b>by </b><i>, <a class="ref" href="cat_1.html#T23">CAT_1:23</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/><b>hence </b><a NAME="E4:66_1"/>
 <a href="cat_1.html#K10">id</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:66"/>
 <a href="cat_1.html#K6">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i>, <a class="ref" href="cat_1.html#T26">CAT_1:26</a></i>;<br/>


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