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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E1:72"/><span class="lab"><font color="Green" title="E52">A1</font></span>: 
 <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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T56" title="CAT_1:th.56">CAT_1:56</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E2:72_1"/><span class="lab"><font color="Green" title="E53">A2</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D19" target="_self" title="NATTRA_1:def.19">Def19</a></span>;<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:72"><span class="lab"><font color="Green" title="E52">A1</font></span></a>, <a class="ref" href="cat_1.html#T23" title="CAT_1:th.23">CAT_1:23</a></span>
<br/>.= 
<font color="Maroon" title="c4">a2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:72_1"><span class="lab"><font color="Green" title="E53">A2</font></span></a>, <a class="ref" href="cat_1.html#T44" title="CAT_1:th.44">CAT_1:44</a></span>
;<br/><span class="kw">hence </span><a NAME="E4:72_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:72_1"><span class="lab"><font color="Green" title="E53">A2</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:72"/>
 <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 class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T26" title="CAT_1:th.26">CAT_1:26</a>, <a class="ref" href="cat_1.html#T56" title="CAT_1:th.56">CAT_1:56</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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