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<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="E1:8"/>
( <font color="Maroon">X</font> is <a href="trees_3.html#V2" target="_self">constituted-FinTrees</a> implies <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="trees_3.html#K2" target="_self">FinTrees</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_1"/><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="finset_1.html#V1">finite</a> <a href="trees_1.html#NM1">Tree</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_3.html#D4" target="_self">TREES_3:def 4</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="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:8_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E3:8_1"/><b>then </b>
<font color="Maroon">x</font> is  <a href="finset_1.html#V1">finite</a> <a href="trees_1.html#NM1">Tree</a>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:8_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="trees_3.html#K2" target="_self">FinTrees</a> 
 <b>by </b><i/>;<br/>


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

<b>assume </b><a NAME="E2:8"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="trees_3.html#K2" target="_self">FinTrees</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#D4" target="_self">TREES_3:def 4</a><br/>

<b>assume </b><a NAME="E3:8"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>

<b>hence </b><a NAME="E4:8"/>
<font color="Maroon">x</font> is  <a href="finset_1.html#V1">finite</a> <a href="trees_1.html#NM1">Tree</a>
 <b>by </b><i>, </i>;<br/>


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