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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="trees_2.html#NM4">DecoratedTree</a>;<br/>



<b>assume </b><a NAME="E1:41"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> is <a href="finset_1.html#V1">finite</a> &amp;  <a href="trees_9.html#K3" target="_self">Subtrees</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="trees_9.html#K3" target="_self">Subtrees</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E2:41"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="trees_9.html#K3" target="_self">Subtrees</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="trees_9.html#T12" target="_self">Th12</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="trees_4.html#NM1">Node</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E4:41"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="trees_2.html#K5">|</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  <a href="finset_1.html#V1">finite</a> <a href="trees_2.html#NM4">DecoratedTree</a> <b>by </b><i><a class="txt" href="trees_9.html#E1:41"><i><font color="Green">E22</font></i></a></i>;<br/>
<a NAME="E6:41"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="trees_9.html#K3" target="_self">Subtrees</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="trees_9.html#E1:41"><i><font color="Green">E22</font></i></a>, <a class="ref" href="trees_9.html#T12" target="_self">Th12</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="trees_4.html#NM1">Node</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E8:41"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="trees_2.html#K5">|</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>
<a NAME="E9:41"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="trees_2.html#K5">|</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="trees_1.html#K4">|</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="trees_2.html#D11">TREES_2:def 11</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>3</sub></font> as    <a href="trees_1.html#M1">Element</a> of  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font> <b>by </b><i><a class="txt" href="trees_9.html#E8:41"><i><font color="Green">E24</font></i></a>, <a class="ref" href="trees_1.html#D9">TREES_1:def 9</a></i>;<br/>
<a NAME="E11:41"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="trees_2.html#K5">|</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="trees_9.html#E4:41"><i><font color="Green">E23</font></i></a>, <a class="txt" href="trees_9.html#E8:41"><i><font color="Green">E24</font></i></a>, <a class="ref" href="trees_9.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E12:41"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="trees_1.html#K4">|</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="trees_2.html#D11">TREES_2:def 11</a></i>;<br/>
<a NAME="E13:41"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="trees_9.html#T10" target="_self">Th10</a></i>;<br/>
<a NAME="E14:41"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#T48">FINSEQ_1:48</a></i>;<br/>
<b>hence </b><a NAME="E15:41"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="trees_9.html#E4:41"><i><font color="Green">E23</font></i></a>, <a class="ref" href="trees_9.html#T1" target="_self">Th1</a></i>;<br/>


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