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

<b>consider </b><font color="Maroon">w</font> being    <a href="trees_1.html#M1">Element</a> of <font color="Maroon">T</font>;<br/>
<b>consider </b><font color="Maroon">X</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:10_1_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">w</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/>
<a NAME="E4:10_1_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">X</font> is <a href="trees_1.html#V2">AntiChain_of_Prefixes-like</a>
 
<b>by </b><i>, <a class="ref" href="trees_1.html#T70">TREES_1:70</a></i>;<br/>
<a NAME="E5:10_1_1"/>
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">T</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1_1_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="E1:10_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E2:10_1_1_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">w</font>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:10_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font>
 ;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">X</font> = <font color="Maroon">X</font> as    <a href="trees_1.html#M4">AntiChain_of_Prefixes</a> of <font color="Maroon">T</font> <b>by </b><i>, <a class="ref" href="trees_1.html#D14">TREES_1:def 14</a></i>;<br/>
<b>take </b>
<font color="Maroon">X</font>
;<br/>

<b>thus </b><a NAME="E7:10_1_1"/>
not <font color="Maroon">X</font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i/>;<br/>


</div>
