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

<b>consider </b><font color="Maroon">f</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="dtconstr.html#K4" target="_self">TS</a> <a href="dtconstr.html#K5" target="_self">PeanoNat</a> ,the <a href="struct_0.html#U1">carrier</a> of <a href="dtconstr.html#K5" target="_self">PeanoNat</a>  <a href="finseq_2.html#K3">*</a> <b> such that </b><br/><a NAME="E2:61"/><i><font color="Green">E31</font></i>: 
(  <a href="dtconstr.html#K18" target="_self">PostTraversal</a> <span class="p1">(<span class="default"><a href="trees_4.html#K2">root-tree</a> <font color="Maroon">O</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K8" target="_self">root-tree</a> <font color="Maroon">O</font></span>)</span> &amp; ( for <font color="Olive">t</font> being  <a href="lang1.html#NM1">Symbol</a> of <a href="dtconstr.html#K5" target="_self">PeanoNat</a>   st <font color="Olive">t</font> <a href="hidden.html#R2">in</a>  <a href="dtconstr.html#K6" target="_self">Terminals</a> <a href="dtconstr.html#K5" target="_self">PeanoNat</a>  holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="trees_4.html#K2">root-tree</a> <font color="Olive">t</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Olive">t</font></span><a href="lang1.html#K3">*&gt;</a></span> ) &amp; ( for <font color="Olive">nt</font> being  <a href="lang1.html#NM1">Symbol</a> of <a href="dtconstr.html#K5" target="_self">PeanoNat</a> <br/> for <font color="Olive">ts</font> being   <a href="trees_4.html#M1">FinSequence</a> of  <a href="dtconstr.html#K4" target="_self">TS</a> <a href="dtconstr.html#K5" target="_self">PeanoNat</a> <br/> for <font color="Olive">rts</font> being  <a href="finseq_1.html#NM1">FinSequence</a>  st <font color="Olive">rts</font> <a href="hidden.html#R1">=</a>  <a href="dtconstr.html#K1" target="_self">roots</a> <font color="Olive">ts</font> &amp; <font color="Olive">nt</font> <a href="lang1.html#R1">==&gt;</a> <font color="Olive">rts</font> holds <br/>for <font color="Olive">x</font> being   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="dtconstr.html#K5" target="_self">PeanoNat</a>  <a href="finseq_2.html#K3">*</a>   st <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="finseqop.html#K5">*</a> <font color="Olive">ts</font> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">nt</font> <a href="trees_4.html#K12">-tree</a> <font color="Olive">ts</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15" target="_self">FlattenSeq</a> <font color="Olive">x</font></span>)</span> <a href="lang1.html#K1">^</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Olive">nt</font></span><a href="lang1.html#K3">*&gt;</a></span> ) )
 <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">rtO</font> =  <a href="dtconstr.html#K8" target="_self">root-tree</a> <font color="Maroon">O</font> as    <a href="dtconstr.html#M1" target="_self">Element</a> of  <a href="dtconstr.html#K4" target="_self">TS</a> <a href="dtconstr.html#K5" target="_self">PeanoNat</a>  ;<br/>
<b>defpred </b><font color="Maroon">S<sub>2</sub></font>[  <a href="trees_2.html#NM6">DecoratedTree</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="dtconstr.html#K5" target="_self">PeanoNat</a> ] <b>means </b> ex <font color="Olive">t</font> being   <a href="dtconstr.html#M1" target="_self">Element</a> of  <a href="dtconstr.html#K4" target="_self">TS</a> <a href="dtconstr.html#K5" target="_self">PeanoNat</a>  st <br/>( <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">t</font> &amp;  <a href="dtconstr.html#K18" target="_self">PostTraversal</a> <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default">0</span><a href="lang1.html#K3">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="trees_1.html#K6">height</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Olive">t</font></span>)</span></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> 1</span>)</span> );<br/>
<div><i><font color="Green">E32</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="61_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">s</font> be   <a href="lang1.html#NM1">Symbol</a> of <a href="dtconstr.html#K5" target="_self">PeanoNat</a> ;<br/><b>assume </b><a NAME="E1:61_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">s</font> <a href="hidden.html#R2">in</a>  <a href="dtconstr.html#K6" target="_self">Terminals</a> <a href="dtconstr.html#K5" target="_self">PeanoNat</a> 
 ;<br/><b>thus </b><a NAME="E2:61_1"/>
<font color="Maroon">S<sub>2</sub></font>[ <a href="trees_4.html#K2">root-tree</a> <font color="Maroon">s</font>]
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_1_1"><b>proof </b></a><div class="add">

<b>take </b><font color="Maroon">t</font> = <font color="Maroon">rtO</font>;<br/>

<b>thus </b><a NAME="E1:61_1_1"/>
 <a href="trees_4.html#K2">root-tree</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font>
 <b>by </b><i><a class="txt" href="dtconstr.html#E5:61"><i><font color="Green">E45</font></i></a>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>

<b>thus </b> <a href="dtconstr.html#K18" target="_self">PostTraversal</a> <font color="Maroon">t</font> = 
<span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">O</font></span><a href="lang1.html#K3">*&gt;</a></span>
<b>by </b><i/>
<br/>.= 
<span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">O</font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>
<br/>.= 
<span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default">0</span><a href="lang1.html#K3">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default">0 <a href="finseqop.html#K4">|-&gt;</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="finseq_2.html#T72">FINSEQ_2:72</a></i>
<br/>.= 
<span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default">0</span><a href="lang1.html#K3">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="trees_1.html#K6">height</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="trees_1.html#T79">TREES_1:79</a>, <a class="ref" href="trees_4.html#T3">TREES_4:3</a></i>
;<br/>


</div><b>end;</b></div></div><b>end;</b></div>
<div><i><font color="Green">E45</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="61_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">nt</font> be   <a href="lang1.html#NM1">Symbol</a> of <a href="dtconstr.html#K5" target="_self">PeanoNat</a> ;<br/><b>let </b><font color="Maroon">ts</font> be    <a href="trees_4.html#M1">FinSequence</a> of  <a href="dtconstr.html#K4" target="_self">TS</a> <a href="dtconstr.html#K5" target="_self">PeanoNat</a> ;<br/><b>assume </b><a NAME="E1:61_2"/><i><font color="Green">E59</font></i>: 
( <font color="Maroon">nt</font> <a href="lang1.html#R1">==&gt;</a>  <a href="dtconstr.html#K1" target="_self">roots</a> <font color="Maroon">ts</font> &amp; ( for <font color="Olive">t</font> being  <a href="trees_2.html#NM6">DecoratedTree</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="dtconstr.html#K5" target="_self">PeanoNat</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">ts</font> holds <br/><font color="Maroon">S<sub>2</sub></font>[<font color="Olive">t</font>] ) )
 ;<br/><b>then reconsider </b><font color="Maroon">t'</font> = <font color="Maroon">nt</font> <a href="trees_4.html#K12">-tree</a> <font color="Maroon">ts</font> as    <a href="dtconstr.html#M1" target="_self">Element</a> of  <a href="dtconstr.html#K4" target="_self">TS</a> <a href="dtconstr.html#K5" target="_self">PeanoNat</a>  <b>by </b><i/>;<br/><a NAME="E3:61_2"/><i><font color="Green">E62</font></i>: 
( <font color="Maroon">nt</font> <a href="hidden.html#R1">=</a> <font color="Maroon">S</font> &amp; (  <a href="dtconstr.html#K1" target="_self">roots</a> <font color="Maroon">ts</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">O</font></span><a href="lang1.html#K3">*&gt;</a></span> or  <a href="dtconstr.html#K1" target="_self">roots</a> <font color="Maroon">ts</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default">1</span><a href="lang1.html#K3">*&gt;</a></span> ) )
 <b>by </b><i><a class="ref" href="dtconstr.html#T7" target="_self">Th7</a>, </i>;<br/><a NAME="E4:61_2"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K1" target="_self">roots</a> <font color="Maroon">ts</font></span>)</span> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/><b>then consider </b><font color="Maroon">x</font> being    <a href="trees_3.html#M5">Element</a> of  <a href="trees_3.html#K5">FinTrees</a> the <a href="struct_0.html#U1">carrier</a> of <a href="dtconstr.html#K5" target="_self">PeanoNat</a> <b> such that </b><br/><a NAME="E6:61_2"/><i><font color="Green">E63</font></i>: 
( <font color="Maroon">ts</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">x</font></span><a href="lang1.html#K3">*&gt;</a></span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="dtconstr.html#K4" target="_self">TS</a> <a href="dtconstr.html#K5" target="_self">PeanoNat</a>  )
 <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x</font> as    <a href="dtconstr.html#M1" target="_self">Element</a> of  <a href="dtconstr.html#K4" target="_self">TS</a> <a href="dtconstr.html#K5" target="_self">PeanoNat</a>  <b>by </b><i/>;<br/><a NAME="E8:61_2"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">ts</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T56">FINSEQ_1:56</a></i>;<br/><a NAME="E9:61_2"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">ts</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E10:61_2"/><b>then </b><i><font color="Green">E64</font></i>: 
 ex <font color="Olive">t'</font> being   <a href="dtconstr.html#M1" target="_self">Element</a> of  <a href="dtconstr.html#K4" target="_self">TS</a> <a href="dtconstr.html#K5" target="_self">PeanoNat</a>  st <br/>( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">t'</font> &amp;  <a href="dtconstr.html#K18" target="_self">PostTraversal</a> <font color="Olive">t'</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">O</font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="trees_1.html#K6">height</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Olive">t'</font></span>)</span></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> 1</span>)</span> )
 <b>by </b><i><a class="ref" href="dtconstr.html#T7" target="_self">Th7</a></i>;<br/><a NAME="E11:61_2"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x'</font> is    <a href="finseq_2.html#M2">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="dtconstr.html#K5" target="_self">PeanoNat</a>  <a href="finseq_2.html#K3">*</a> 
 ;<br/><a NAME="E12:61_2"/><b>then </b><i><font color="Green">E75</font></i>: 
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x'</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">O</font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="trees_1.html#K6">height</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">x'</font></span>)</span></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> 1</span>)</span>
 <b>by </b><i>, , </i>;<br/><a NAME="E13:61_2"/>
<font color="Maroon">f</font> <a href="finseqop.html#K5">*</a> <font color="Maroon">ts</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span></span><a href="finseq_1.html#K9">*&gt;</a></span>
 <b>by </b><i>, <a class="ref" href="finseq_2.html#T39">FINSEQ_2:39</a></i>;<br/><b>then </b><i><font color="Green">E76</font></i>: <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">nt</font> <a href="trees_4.html#K12">-tree</a> <font color="Maroon">ts</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="dtconstr.html#K15" target="_self">FlattenSeq</a> <span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x'</font></span>)</span></span><a href="lang1.html#K3">*&gt;</a></span></span>)</span> <a href="lang1.html#K1">^</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">nt</font></span><a href="lang1.html#K3">*&gt;</a></span>
<b>by </b><i>, <a class="ref" href="dtconstr.html#T7" target="_self">Th7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">O</font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="trees_1.html#K6">height</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">x'</font></span>)</span></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">nt</font></span><a href="lang1.html#K3">*&gt;</a></span>
<b>by </b><i>, <a class="txt" href="dtconstr.html#E3"><i><font color="Green">Lemma36</font></i></a></i>
<br/>.= 
<span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">O</font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="trees_1.html#K6">height</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">x'</font></span>)</span></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> 1</span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">nt</font></span><a href="lang1.html#K3">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>
<br/>.= 
<span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">O</font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="trees_1.html#K6">height</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">x'</font></span>)</span></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> 1</span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default">1 <a href="finseqop.html#K4">|-&gt;</a> 1</span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="finseq_2.html#T73">FINSEQ_2:73</a></i>
<br/>.= 
<span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">O</font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="trees_1.html#K6">height</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">x'</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="finseqop.html#K4">|-&gt;</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="finseq_2.html#T143">FINSEQ_2:143</a></i>
<br/>.= 
<span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">O</font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="trees_1.html#K6">height</a> <span class="p3">(<span class="default"><a href="trees_3.html#K14">^</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">x'</font></span>)</span></span>)</span></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="trees_3.html#T83">TREES_3:83</a></i>
;<br/><a NAME="E15:61_2"/><i><font color="Green">E77</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">nt</font> <a href="trees_4.html#K9">-tree</a> <font color="Maroon">x'</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="trees_3.html#K14">^</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">x'</font></span>)</span> &amp; <font color="Maroon">t'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">nt</font> <a href="trees_4.html#K9">-tree</a> <font color="Maroon">x'</font> )
 <b>by </b><i>, <a class="ref" href="trees_4.html#T13">TREES_4:13</a>, <a class="ref" href="trees_4.html#D5">TREES_4:def 5</a></i>;<br/><a NAME="E16:61_2"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">t'</font> is    <a href="finseq_2.html#M2">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="dtconstr.html#K5" target="_self">PeanoNat</a>  <a href="finseq_2.html#K3">*</a> 
 ;<br/><a NAME="E17:61_2"/><b>then </b>
 <a href="dtconstr.html#K18" target="_self">PostTraversal</a> <span class="p1">(<span class="default"><font color="Maroon">nt</font> <a href="trees_4.html#K12">-tree</a> <font color="Maroon">ts</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">nt</font> <a href="trees_4.html#K12">-tree</a> <font color="Maroon">ts</font></span>)</span>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E18:61_2"/>
<font color="Maroon">S<sub>2</sub></font>[<font color="Maroon">nt</font> <a href="trees_4.html#K12">-tree</a> <font color="Maroon">ts</font>]
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<a NAME="E6:61"/><i><font color="Green">E80</font></i>: 
for <font color="Olive">t</font> being  <a href="trees_2.html#NM6">DecoratedTree</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="dtconstr.html#K5" target="_self">PeanoNat</a>   st <font color="Olive">t</font> <a href="hidden.html#R2">in</a>  <a href="dtconstr.html#K4" target="_self">TS</a> <a href="dtconstr.html#K5" target="_self">PeanoNat</a>  holds <br/><font color="Maroon">S<sub>2</sub></font>[<font color="Olive">t</font>]
 
<b>from </b><i><a class="ref" href="dtconstr.html#S7" target="_self">DTCONSTR:sch 7</a>(, <a class="txt" href="dtconstr.html#E5:61"><i><font color="Green">E45</font></i></a>);<br/></i>
<b>let </b><font color="Maroon">t</font> be    <a href="dtconstr.html#M1" target="_self">Element</a> of  <a href="dtconstr.html#K4" target="_self">TS</a> <a href="dtconstr.html#K5" target="_self">PeanoNat</a> ;<br/>

<a NAME="E7:61"/>
<font color="Maroon">S<sub>2</sub></font>[<font color="Maroon">t</font>]
 
<b>by </b><i><a class="ref" href="dtconstr.html#T7" target="_self">Th7</a></i>;<br/>
<b>hence </b><a NAME="E8:61"/>
 <a href="dtconstr.html#K18" target="_self">PostTraversal</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default">0</span><a href="lang1.html#K3">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="trees_1.html#K6">height</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> 1</span>)</span>
 ;<br/>


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