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

<b>let </b><font color="Maroon" title="c1">fT</font> be  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a>;<br/>

<b>assume </b><a NAME="E1:70"/><i><font color="Green" title="E41">A1</font></i>: 
 <a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <font color="Maroon" title="c1">fT</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/>

<b>thus </b><a NAME="E2:70"/>
<font color="Maroon" title="c1">fT</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> 0
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">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" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:70_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">fT</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c3">t</font> = <font color="Maroon" title="c2">x</font> as    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of <font color="Maroon" title="c1">fT</font> ;<br/>
<a NAME="E3:70_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">t</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 0 &amp; 0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">t</font> )
 
<b>by </b><i><a class="txt" href="trees_1.html#E1:70"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="trees_1.html#D15" target="_self" title="TREES_1:def.15">Def15</a></i>;<br/>
<a NAME="E4:70_1"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 
;<br/>
<a NAME="E5:70_1"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#T25" title="FINSEQ_1:th.25">FINSEQ_1:25</a></i>;<br/>
<b>hence </b><a NAME="E6:70_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> 0
 <b>by </b><i><a class="ref" href="trees_1.html#T47" target="_self" title="TREES_1:th.47">Th47</a></i>;<br/>


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

<b>let </b><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E3:70"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> 0
 ;<br/>

<a NAME="E4:70"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="trees_1.html#T56" target="_self" title="TREES_1:th.56">Th56</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:70"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">fT</font>
 <b>by </b><i><a class="ref" href="trees_1.html#T47" target="_self" title="TREES_1:th.47">Th47</a></i>;<br/>


</div>
