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<b>let </b><font color="Maroon" title="c1">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">F</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="trees_3.html#K5" title="TREES_3:func.5">FinTrees</a> <font color="Maroon" title="c1">D</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c3">p</font> be    <a href="trees_4.html#M1" title="TREES_4:mode.1">FinSequence</a> of <font color="Maroon" title="c2">F</font>;<br/>





<b>assume </b><a NAME="E1:9"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/>

<a NAME="E2:9"/><b>then </b><i><font color="Green" title="E7">A1</font></i>: 
(  <a href="finsop_1.html#K5" title="FINSOP_1:func.5">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 1 &amp;  <a href="finsop_1.html#K5" title="FINSOP_1:func.5">dom</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finsop_1.html#K5" title="FINSOP_1:func.5">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Maroon" title="c3">p</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a>, <a class="ref" href="trees_3.html#D18" title="TREES_3:def.18">TREES_3:def 18</a></i>;<br/>
<a NAME="E3:9"/><b>then </b><i><font color="Green" title="E8">A2</font></i>: 
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finsop_1.html#K5" title="FINSOP_1:func.5">dom</a> <font color="Maroon" title="c3">p</font>
 
;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">x</font> = <font color="Maroon" title="c3">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 as    <a href="trees_3.html#M5" title="TREES_3:mode.5">Element</a> of  <a href="trees_3.html#K5" title="TREES_3:func.5">FinTrees</a> <font color="Maroon" title="c1">D</font> <b>by </b><i><a class="ref" href="dtconstr.html#T2" target="_self" title="DTCONSTR:th.2">Th2</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">x</font>
;<br/>

<b>thus </b><a NAME="E5:9"/>
( <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c4">x</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span> &amp; <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> )
 <b>by </b><i><a class="txt" href="dtconstr.html#E2:9"><i><font color="Green" title="E7">A1</font></i></a>, <a class="txt" href="dtconstr.html#E3:9"><i><font color="Green" title="E8">A2</font></i></a>, <a class="ref" href="dtconstr.html#T2" target="_self" title="DTCONSTR:th.2">Th2</a>, <a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></i>;<br/>


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