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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="trees_2.html#NM4">DecoratedTree</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="trees_4.html#NM1">Node</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>





<b>assume </b><a NAME="E1:42"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="trees_9.html#K3" target="_self">Subtrees</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>2</sub></font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="trees_4.html#NM1">Node</a> of <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>2</sub></font></span>)</span><b> such that </b><br/><a NAME="E3:42"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</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>2</sub></font></span>)</span> <a href="trees_2.html#K5">|</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>
<a NAME="E4:42"/>
 <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>2</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>2</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>5</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="trees_4.html#NM1">Node</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="trees_1.html#D9">TREES_1:def 9</a></i>;<br/>
<a NAME="E6:42"/>
<font color="Maroon">c<sub>3</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>
 
<b>by </b><i><a class="txt" href="trees_9.html#E3:42"><i><font color="Green">E22</font></i></a>, <a class="ref" href="trees_9.html#T3" target="_self">Th3</a></i>;<br/>
<b>hence </b><a NAME="E7:42"/>
<font color="Maroon">c<sub>3</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>
 ;<br/>


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