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<div class="add">

<a NAME="E1:37_1_1"/>
 <a href="trees_9.html#K3" title="TREES_9:func.3">Subtrees</a> <font color="Maroon" title="c2">t</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="trees_3.html#K4" title="TREES_3:func.4">Trees</a> <font color="Maroon" title="c1">D</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:37_1_1_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_9.html#K3" title="TREES_9:func.3">Subtrees</a> <font color="Maroon" title="c2">t</font>
 ;<br/>

<a NAME="E2:37_1_1_1"/><b>then </b>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="trees_2.html#K7" title="TREES_2:func.7">|</a> <font color="Olive" title="b1">p</font></span>)</span> where <font color="Olive" title="b1">p</font> is   <a href="trees_4.html#NM1" title="TREES_4:NM.1">Node</a> of <font color="Maroon" title="c2">t</font> : verum </span>}</span> 
 
;<br/>
<a NAME="E3:37_1_1_1"/><b>then </b>
 ex <font color="Olive" title="b1">p</font> being  <a href="trees_4.html#NM1" title="TREES_4:NM.1">Node</a> of <font color="Maroon" title="c2">t</font> st <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">t</font> <a href="trees_2.html#K7" title="TREES_2:func.7">|</a> <font color="Olive" title="b1">p</font>
 
;<br/>
<b>hence </b><a NAME="E4:37_1_1_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_3.html#K4" title="TREES_3:func.4">Trees</a> <font color="Maroon" title="c1">D</font>
 <b>by </b><i><a class="ref" href="trees_3.html#D7" title="TREES_3:def.7">TREES_3:def 7</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:37_1_1"/>
 <a href="trees_9.html#K3" title="TREES_9:func.3">Subtrees</a> <font color="Maroon" title="c2">t</font> is  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <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#K4" title="TREES_3:func.4">Trees</a> <font color="Maroon" title="c1">D</font></span>)</span>
 ;<br/>


</div>
