<?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>thus </b><a NAME="E1:21"/>
( <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> is <a href="trees_3.html#V3" target="_self">constituted-DTrees</a> implies <font color="Maroon">x</font> is   <a href="trees_2.html#NM4">DecoratedTree</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:21_1"/><i><font color="Green">E39</font></i>: 
for <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> holds <br/><font color="Olive">y</font> is   <a href="trees_2.html#NM4">DecoratedTree</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_3.html#D5" target="_self">TREES_3:def 5</a><br/>

<a NAME="E2:21_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:21_1"/>
<font color="Maroon">x</font> is   <a href="trees_2.html#NM4">DecoratedTree</a>
 <b>by </b><i/>;<br/>


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

<b>assume </b><a NAME="E2:21"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">x</font> is   <a href="trees_2.html#NM4">DecoratedTree</a>
 ;<br/>

<b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_3.html#D5" target="_self">TREES_3:def 5</a><br/>

<b>thus </b><a NAME="E3:21"/>
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> implies <font color="Maroon">y</font> is   <a href="trees_2.html#NM4">DecoratedTree</a> )
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


</div>
