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

<b>let </b><font color="Maroon">A</font> be   <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>, <font color="Maroon">b</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font>, <font color="Maroon">c</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font>, <font color="Maroon">d</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font>;<br/>



<b>assume </b><a NAME="E1:21"/>
 <a href="cat_1.html#K6">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:21"/><i><font color="Green">E7</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">c</font>,<font color="Maroon">d</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">A</font> <b>by </b><i><a class="ref" href="nattra_1.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E5:21"/>
(  <a href="cat_1.html#K2">dom</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp;  <a href="cat_1.html#K3">cod</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp;  <a href="cat_1.html#K2">dom</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp;  <a href="cat_1.html#K3">cod</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 
<b>by </b><i><a class="ref" href="nattra_1.html#T1" target="_self">Th1</a>, <a class="ref" href="cat_1.html#T18">CAT_1:18</a></i>;<br/>
<b>hence </b><a NAME="E6:21"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 ;<br/>


</div>
