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

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



<b>assume </b><b>that </b><br/><a NAME="E1:148"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">w</font>
 <b>and </b><br/><a NAME="E2:148"/><i><font color="Green">E40</font></i>: 
for <font color="Olive">t'</font> being <a href="finset_1.html#V1">finite</a> <a href="trees_1.html#NM1">Tree</a>  st <font color="Olive">t'</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">w</font> holds <br/> <a href="trees_1.html#K6">height</a> <font color="Olive">t'</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="trees_1.html#K6">height</a> <font color="Maroon">t</font>
 ;<br/>

<a NAME="E3:148"/>
 <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">w</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a>  <a href="trees_1.html#K6">height</a> <font color="Maroon">t</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:148"/><b>then </b>
(  <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">w</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="trees_1.html#K6">height</a> <font color="Maroon">t</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 &amp;  <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">w</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="trees_1.html#K6">height</a> <font color="Maroon">t</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 )
 
<b>by </b><i><a class="ref" href="trees_3.html#D7" target="_self">Def7</a>, <a class="ref" href="trees_3.html#D6" target="_self">Def6</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<b>hence </b><a NAME="E5:148"/>
 <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">w</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="trees_1.html#K6">height</a> <font color="Maroon">t</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>


</div>
