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<div class="add">

<b>let </b><font color="Maroon">fT</font> be  <a href="finset_1.html#V1">finite</a> <a href="trees_1.html#NM1">Tree</a>;<br/>

<b>assume </b><a NAME="E1:70"/><i><font color="Green">E28</font></i>: 
 <a href="trees_1.html#K6" target="_self">height</a> <font color="Maroon">fT</font> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<b>thus </b><a NAME="E2:70"/>
<font color="Maroon">fT</font> <a href="tarski.html#R1">c=</a>  <a href="trees_1.html#K2" target="_self">elementary_tree</a> 0
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_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="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:70_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">fT</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">t</font> = <font color="Maroon">x</font> as    <a href="trees_1.html#M1" target="_self">Element</a> of <font color="Maroon">fT</font> ;<br/>
<a NAME="E3:70_1"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">t</font> <a href="xxreal_0.html#R1">&lt;=</a> 0 &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">t</font> )
 
<b>by </b><i><a class="ref" href="trees_1.html#T8" target="_self">Th8</a>, <a class="ref" href="trees_1.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E4:70_1"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E5:70_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/>
<b>hence </b><a NAME="E6:70_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="trees_1.html#K2" target="_self">elementary_tree</a> 0
 <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="E3:70"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="trees_1.html#K2" target="_self">elementary_tree</a> 0
 ;<br/>

<a NAME="E4:70"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:70"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">fT</font>
 <b>by </b><i/>;<br/>


</div>
