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

<b>let </b><font color="Maroon">C</font> be  <a href="cat_1.html#V1">strict</a> <a href="cat_1.html#NM4">Category</a>;<br/>

<b>assume </b><a NAME="E1:76"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">C</font> is <a href="nattra_1.html#V2" target="_self">discrete</a>
 ;<br/>

<a NAME="E2:76"/>
the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font> <a href="tarski.html#R1">c=</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> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_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="E1:76_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font>
 ;<br/>

<a NAME="E2:76_1"/><b>then </b>
 ex <font color="Olive">a</font> being  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font> st <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10">id</a> <font color="Olive">a</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E3:76_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</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><b>end;</b></div>
<a NAME="E3:76"/><b>then </b><i><font color="Green">E8</font></i>: 
the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font> <a href="tarski.html#R1">c=</a> the <a href="cat_1.html#U2">Morphisms</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" target="_self">IdCat</a> <font color="Maroon">C</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E4:76"/>
the <a href="cat_1.html#U2">Morphisms</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" target="_self">IdCat</a> <font color="Maroon">C</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>by </b><i><a class="ref" href="cat_2.html#T13">CAT_2:13</a></i>;<br/>
<a NAME="E5:76"/><b>then </b><i><font color="Green">E25</font></i>: 
the <a href="cat_1.html#U2">Morphisms</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" target="_self">IdCat</a> <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<a NAME="E6:76"/>
the <a href="cat_1.html#U1">Objects</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" target="_self">IdCat</a> <font color="Maroon">C</font></span>)</span> <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/>;<br/>
<b>hence </b><a NAME="E7:76"/>
 <a href="nattra_1.html#K13" target="_self">IdCat</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 <b>by </b><i>, </i>;<br/>


</div>
