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<b>let </b><font color="Maroon" title="c1">A</font> be  <a href="nattra_1.html#V2" title="NATTRA_1:attr.2">discrete</a> <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> holds   <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">a</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/><b>let </b><font color="Maroon" title="c2">a</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c2">a</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/>



<a NAME="E1:65"/><i><font color="Green" title="E52">A1</font></i>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="cat_1.html#T56" title="CAT_1:th.56">CAT_1:56</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">g</font> be    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font></span><br/><b>consider </b><font color="Maroon" title="c4">a2</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font><b> such that </b><br/><a NAME="E2:65_1"/><i><font color="Green" title="E53">A2</font></i>: 
<font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c4">a2</font>
 <b>by </b><i><a class="ref" href="nattra_1.html#D19" target="_self" title="NATTRA_1:def.19">Def19</a></i>;<br/><font color="Maroon" title="c2">a</font> = 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c3">g</font>
<b>by </b><i><a class="txt" href="#E1:65"><i><font color="Green" title="E52">A1</font></i></a>, <a class="ref" href="cat_1.html#T23" title="CAT_1:th.23">CAT_1:23</a></i>
<br/>.= 
<font color="Maroon" title="c4">a2</font>
<b>by </b><i><a class="txt" href="#E2:65_1"><i><font color="Green" title="E53">A2</font></i></a>, <a class="ref" href="cat_1.html#T44" title="CAT_1:th.44">CAT_1:44</a></i>
;<br/><b>hence </b><a NAME="E4:65_1"/>
 <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font>
 <b>by </b><i><a class="txt" href="#E2:65_1"><i><font color="Green" title="E53">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:65"/>
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c2">a</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="#E1:65"><i><font color="Green" title="E52">A1</font></i></a>, <a class="ref" href="cat_1.html#T26" title="CAT_1:th.26">CAT_1:26</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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