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<b>let </b><font color="Maroon">t</font> be   <a href="trees_2.html#NM4">DecoratedTree</a>;<br/>

<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a>
<div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:57_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="trees_9.html#K9" target="_self">Subtrees</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">t</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><b>then consider </b><font color="Maroon">u</font> being    <a href="trees_3.html#M3">Element</a> of <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">t</font></span><a href="tarski.html#K1">}</a></span>, <font color="Maroon">p</font> being   <a href="trees_4.html#NM1">Node</a> of <font color="Maroon">u</font><b> such that </b><br/><a NAME="E3:57_1"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u</font> <a href="trees_2.html#K5">|</a> <font color="Maroon">p</font>
 ;<br/><a NAME="E4:57_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E5:57_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="trees_9.html#K3" target="_self">Subtrees</a> <font color="Maroon">t</font>
 <b>by </b><i/>;<br/></div>
<b>end;</b></div>

<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="E2:57"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="trees_9.html#K3" target="_self">Subtrees</a> <font color="Maroon">t</font>
 ;<br/>

<a NAME="E3:57"/><b>then </b>
( <font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">t</font></span><a href="tarski.html#K1">}</a></span> &amp;  ex <font color="Olive">p</font> being  <a href="trees_4.html#NM1">Node</a> of <font color="Maroon">t</font> st <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="trees_2.html#K5">|</a> <font color="Olive">p</font> )
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:57"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="trees_9.html#K9" target="_self">Subtrees</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">t</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/>


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