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

<a NAME="E1:38_1_1"/>
 <a href="trees_9.html#K4" target="_self">Subtrees</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="trees_3.html#K5">FinTrees</a> <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></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="E1:38_1_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="trees_9.html#K4" target="_self">Subtrees</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:38_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="trees_2.html#K7">|</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="trees_4.html#NM1">Node</a> of <font color="Maroon">c<sub>2</sub></font> : verum </span>}</span> 
 
;<br/>
<a NAME="E3:38_1_1_1"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="trees_4.html#NM1">Node</a> of <font color="Maroon">c<sub>2</sub></font> st <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="trees_2.html#K7">|</a> <font color="Olive">b<sub>1</sub></font>
 
;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as  <a href="finset_1.html#V1">finite</a> <a href="trees_2.html#NM6">DecoratedTree</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E5:38_1_1_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font> is <a href="finset_1.html#V1">finite</a>
 
;<br/>
<b>hence </b><a NAME="E6:38_1_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="trees_3.html#K5">FinTrees</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="trees_3.html#D8">TREES_3:def 8</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:38_1_1"/>
 <a href="trees_9.html#K3" target="_self">Subtrees</a> <font color="Maroon">c<sub>2</sub></font> is  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="trees_3.html#K5">FinTrees</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/>


</div>
