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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="trees_3.html#V5" target="_self">FinTree-yielding</a> <a href="finseq_1.html#NM1">FinSequence</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="finset_1.html#V1">finite</a> <a href="trees_1.html#NM1">Tree</a>;<br/>



<b>assume </b><a NAME="E1:147"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:147"/><i><font color="Green">E60</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="trees_3.html#E3:147"><i><font color="Green">E60</font></i></a></i>;<br/>
<a NAME="E5:147"/><i><font color="Green">E61</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="trees_3.html#E3:147"><i><font color="Green">E60</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E7:147"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 1 <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#T28">NAT_1:28</a></i>;<br/>
<a NAME="E8:147"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> )
 
<b>by </b><i><a class="txt" href="trees_3.html#E5:147"><i><font color="Green">E61</font></i></a>, <a class="txt" href="trees_3.html#E7:147"><i><font color="Green">E62</font></i></a>, <a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a>, <a class="ref" href="trees_1.html#T47">TREES_1:47</a></i>;<br/>
<a NAME="E9:147"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="trees_3.html#K13" target="_self">tree</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="trees_1.html#K4">|</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> &amp; <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="trees_3.html#K13" target="_self">tree</a> <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="txt" href="trees_3.html#E3:147"><i><font color="Green">E60</font></i></a>, <a class="txt" href="trees_3.html#E7:147"><i><font color="Green">E62</font></i></a>, <a class="ref" href="trees_3.html#D15" target="_self">Def15</a>, <a class="ref" href="trees_3.html#T52" target="_self">Th52</a></i>;<br/>
<b>hence </b><a NAME="E10:147"/>
 <a href="trees_1.html#K6">height</a> <span class="p1">(<span class="default"><a href="trees_3.html#K13" target="_self">tree</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a>  <a href="trees_1.html#K6">height</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="trees_1.html#T85">TREES_1:85</a></i>;<br/>


</div>
