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

<b>let </b><font color="Maroon" title="c1">Y</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">z0</font>, <font color="Maroon" title="c4">t</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c5">PA</font>, <font color="Maroon" title="c6">PC</font> be    <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">Y</font>;<br/>









<b>assume </b><a NAME="E1:25"/><i><font color="Green" title="E19">A1</font></i>: 
( <font color="Maroon" title="c5">PA</font> <a href="partit1.html#NR1" title="PARTIT1:NR.1">'&lt;'</a> <font color="Maroon" title="c6">PC</font> &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">PC</font> &amp; <font color="Maroon" title="c3">z0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">PA</font> &amp; <font color="Maroon" title="c4">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c4">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">z0</font> )
 ;<br/>

<b>then consider </b><font color="Maroon" title="c7">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:25"/><i><font color="Green" title="E20">A2</font></i>: 
( <font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">PC</font> &amp; <font color="Maroon" title="c3">z0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">b</font> )
 <b>by </b><i><a class="ref" href="setfam_1.html#D2" title="SETFAM_1:def.2">SETFAM_1:def 2</a></i>;<br/>
<a NAME="E4:25"/>
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font> or <font color="Maroon" title="c2">x</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c7">b</font> )
 
<b>by </b><i><a class="txt" href="partit1.html#E1:25"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="partit1.html#E3:25"><i><font color="Green" title="E20">A2</font></i></a>, <a class="ref" href="eqrel_1.html#D6" title="EQREL_1:def.6">EQREL_1:def 6</a></i>;<br/>
<b>hence </b><a NAME="E5:25"/>
<font color="Maroon" title="c3">z0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">x</font>
 <b>by </b><i><a class="txt" href="partit1.html#E1:25"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="partit1.html#E3:25"><i><font color="Green" title="E20">A2</font></i></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>;<br/>


</div>
