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

<b>let </b><font color="Maroon">T</font> be   <a href="trees_1.html#NM1">Tree</a>;<br/><b>let </b><font color="Maroon">t1</font> be    <a href="trees_1.html#M1" target="_self">Element</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">t2</font> be    <a href="trees_1.html#M1" target="_self">Element</a> of <font color="Maroon">T</font>;<br/>





<b>assume </b><a NAME="E1:65"/>
not <font color="Maroon">t1</font>,<font color="Maroon">t2</font> <a href="xboole_0.html#R3">are_c=-comparable</a> 
 ;<br/>

<b>then reconsider </b><font color="Maroon">A</font> = <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">t1</font>,<font color="Maroon">t2</font></span><a href="tarski.html#K2">}</a></span> as   <a href="trees_1.html#NM5">AntiChain_of_Prefixes</a> <b>by </b><i/>;<br/>
<a NAME="E3:65"/>
<font color="Maroon">A</font> is    <a href="trees_1.html#M4" target="_self">AntiChain_of_Prefixes</a> of <font color="Maroon">T</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_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>,<a class="ref" href="trees_1.html#D14" target="_self">TREES_1:def 14</a><br/>

<b>assume </b><a NAME="E1:65_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E2:65_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t1</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t2</font> )
 
<b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<b>hence </b><a NAME="E3:65_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>hence </b><a NAME="E4:65"/>
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">t1</font>,<font color="Maroon">t2</font></span><a href="tarski.html#K2">}</a></span> is    <a href="trees_1.html#M4" target="_self">AntiChain_of_Prefixes</a> of <font color="Maroon">T</font>
 ;<br/>


</div>
