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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="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>





<b>assume </b><a NAME="E1:27"/><i><font color="Green">E15</font></i>: 
 <a href="trees_4.html#K1" target="_self">root-tree</a> <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_4.html#K3" target="_self">-flat_tree</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>thus </b><font color="Maroon">c<sub>1</sub></font> = 
<span class="p1">(<span class="default"><a href="trees_4.html#K1" target="_self">root-tree</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="trees_4.html#T3" target="_self">Th3</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="trees_4.html#E1:27"><i><font color="Green">E15</font></i></a>, <a class="ref" href="trees_4.html#D3" target="_self">Def3</a></i>
;<br/>

<a NAME="E3:27"/>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="trees_4.html#K3" target="_self">-flat_tree</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="trees_1.html#K2">elementary_tree</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="trees_4.html#K1" target="_self">root-tree</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="trees_1.html#K2">elementary_tree</a> 0 )
 
<b>by </b><i><a class="ref" href="trees_4.html#D3" target="_self">Def3</a>, <a class="ref" href="trees_4.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E4:27"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="trees_4.html#E1:27"><i><font color="Green">E15</font></i></a>, <a class="ref" href="trees_4.html#T2" target="_self">Th2</a></i>;<br/>
<b>hence </b><a NAME="E5:27"/>
<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#T25">FINSEQ_1:25</a></i>;<br/>


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