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

<b>let </b><font color="Maroon">T1</font> be   <a href="trees_2.html#NM4">DecoratedTree</a>, <font color="Maroon">T2</font> be   <a href="trees_2.html#NM4">DecoratedTree</a>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:14_1"/>
( <font color="Maroon">T1</font> is <a href="bintree1.html#V2" target="_self">binary</a> &amp; <font color="Maroon">T2</font> is <a href="bintree1.html#V2" target="_self">binary</a> )
 ;<br/><a NAME="E2:14_1"/><b>then </b>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">T1</font> is <a href="bintree1.html#V1" target="_self">binary</a> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">T2</font> is <a href="bintree1.html#V1" target="_self">binary</a> )
 <b>by </b><i/>;<br/><a NAME="E3:14_1"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="trees_3.html#K15">tree</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">T1</font></span>)</span>,<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">T2</font></span>)</span> is <a href="bintree1.html#V1" target="_self">binary</a>
 <b>by </b><i/>;<br/><a NAME="E4:14_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="trees_4.html#K6">-tree</a> <font color="Maroon">T1</font>,<font color="Maroon">T2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="trees_3.html#K15">tree</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">T1</font></span>)</span>,<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">T2</font></span>)</span>
 <b>by </b><i><a class="ref" href="trees_4.html#T14">TREES_4:14</a></i>;<br/><b>hence </b><a NAME="E5:14_1"/>
<font color="Maroon">x</font> <a href="trees_4.html#K6">-tree</a> <font color="Maroon">T1</font>,<font color="Maroon">T2</font> is <a href="bintree1.html#V2" target="_self">binary</a>
 <b>by </b><i>, </i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:14"/>
<font color="Maroon">x</font> <a href="trees_4.html#K6">-tree</a> <font color="Maroon">T1</font>,<font color="Maroon">T2</font> is <a href="bintree1.html#V2" target="_self">binary</a>
 ;<br/>

<a NAME="E3:14"/><b>then </b><i><font color="Green">E30</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="trees_4.html#K6">-tree</a> <font color="Maroon">T1</font>,<font color="Maroon">T2</font></span>)</span> is <a href="bintree1.html#V1" target="_self">binary</a>
 
<b>by </b><i/>;<br/>
<a NAME="E4:14"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="trees_4.html#K6">-tree</a> <font color="Maroon">T1</font>,<font color="Maroon">T2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="trees_3.html#K15">tree</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">T1</font></span>)</span>,<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">T2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="trees_4.html#T14">TREES_4:14</a></i>;<br/>
<a NAME="E5:14"/><b>then </b>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">T1</font> is <a href="bintree1.html#V1" target="_self">binary</a> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">T2</font> is <a href="bintree1.html#V1" target="_self">binary</a> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:14"/>
( <font color="Maroon">T1</font> is <a href="bintree1.html#V2" target="_self">binary</a> &amp; <font color="Maroon">T2</font> is <a href="bintree1.html#V2" target="_self">binary</a> )
 <b>by </b><i/>;<br/>


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