<?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">t</font> be    <a href="trees_1.html#M1">Element</a> of <font color="Maroon">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_3.html#D14" target="_self">TREES_3:def 14</a><br/>



<b>assume </b><a NAME="E1:102"/><i><font color="Green">E39</font></i>: 
not <font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="trees_1.html#K2">elementary_tree</a> 0
 ;<br/>

<b>consider </b><font color="Maroon">l</font> being    <a href="trees_3.html#M8" target="_self">Leaf</a> of  <a href="trees_1.html#K2">elementary_tree</a> 0;<br/>
<b>take </b>
<font color="Maroon">l</font>
;<br/>

<a NAME="E3:102"/>
( <font color="Maroon">l</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">t</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="xboole_0.html#K1">{}</a>  <a href="tarski.html#R1">is_a_prefix_of</a> <font color="Maroon">t</font> )
 
<b>by </b><i><a class="ref" href="trees_3.html#D3" target="_self">Def3</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a>, <a class="ref" href="trees_1.html#T56">TREES_1:56</a>, <a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/>
<b>hence </b><a NAME="E4:102"/>
<font color="Maroon">l</font> <a href="trees_1.html#NR3" target="_self">is_a_proper_prefix_of</a> <font color="Maroon">t</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D8">XBOOLE_0:def 8</a></i>;<br/>


</div>
