<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">C</font> be  <a href="cat_1.html#V1" title="CAT_1:attr.1">strict</a> <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>;<br/>

<b>assume </b><a NAME="E1:75"/><i><font color="Green" title="E58">A1</font></i>: 
<font color="Maroon" title="c1">C</font> is <a href="nattra_1.html#V2" title="NATTRA_1:attr.2">discrete</a>
 ;<br/>

<a NAME="E2:75"/>
the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c1">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font> : verum </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:75_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c1">C</font>
 ;<br/>

<a NAME="E2:75_1"/><b>then </b>
 ex <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">C</font> st <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Olive" title="b1">a</font>
 
<b>by </b><i><a class="txt" href="nattra_1.html#E1:75"><i><font color="Green" title="E58">A1</font></i></a>, <a class="ref" href="nattra_1.html#D19" target="_self" title="NATTRA_1:def.19">Def19</a></i>;<br/>
<b>hence </b><a NAME="E3:75_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font> : verum </span>}</span> 
 ;<br/>


</div><b>end;</b></div>
<a NAME="E3:75"/><b>then </b><i><font color="Green" title="E59">A2</font></i>: 
the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c1">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">C</font></span>)</span>
 
<b>by </b><i><a class="ref" href="nattra_1.html#D20" target="_self" title="NATTRA_1:def.20">Def20</a></i>;<br/>
<a NAME="E4:75"/>
the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="ref" href="cat_2.html#T13" title="CAT_2:th.13">CAT_2:13</a></i>;<br/>
<a NAME="E5:75"/><b>then </b><i><font color="Green" title="E60">A3</font></i>: 
the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="txt" href="nattra_1.html#E3:75"><i><font color="Green" title="E59">A2</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/>
<a NAME="E6:75"/>
the <a href="cat_1.html#U1" title="CAT_1:sel.1">Objects</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="ref" href="nattra_1.html#D20" target="_self" title="NATTRA_1:def.20">Def20</a></i>;<br/>
<b>hence </b><a NAME="E7:75"/>
 <a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="nattra_1.html#E5:75"><i><font color="Green" title="E60">A3</font></i></a>, <a class="ref" href="nattra_1.html#T10" target="_self" title="NATTRA_1:th.10">Th10</a></i>;<br/>


</div>
