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

<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:11"/><i><font color="Green">E39</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> holds <br/><font color="Olive">x</font> is   <a href="trees_1.html#NM1">Tree</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_3.html#D3" target="_self">TREES_3:def 3</a><br/>

<b>thus </b><a NAME="E2:11"/>
<font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">Y</font> is <a href="trees_3.html#V1" target="_self">constituted-Trees</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_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="trees_3.html#D3" target="_self">TREES_3:def 3</a><br/>

<b>assume </b><a NAME="E1:11_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">Y</font>
 ;<br/>

<a NAME="E2:11_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E3:11_1"/>
<font color="Maroon">x</font> is   <a href="trees_1.html#NM1">Tree</a>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>

<b>hence </b><a NAME="E3:11"/>
<font color="Maroon">Y</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">X</font> is <a href="trees_3.html#V1" target="_self">constituted-Trees</a>
 ;<br/>

<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="trees_3.html#D3" target="_self">TREES_3:def 3</a><br/>

<b>assume </b><a NAME="E4:11"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">Y</font>
 ;<br/>

<a NAME="E5:11"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 
;<br/>
<b>hence </b><a NAME="E6:11"/>
<font color="Maroon">x</font> is   <a href="trees_1.html#NM1">Tree</a>
 <b>by </b><i/>;<br/>


</div>
