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<b>let </b><font color="Maroon" title="c1">t</font> be   <a href="trees_2.html#NM4" title="TREES_2:NM.4">DecoratedTree</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">X</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="trees_3.html#V3" title="TREES_3:attr.3">constituted-DTrees</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon" title="c1">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">X</font> holds <br/><font color="Maroon" title="c1">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_9.html#K9" title="TREES_9:func.9">Subtrees</a> <font color="Olive" title="b1">X</font></span><br/><b>let </b><font color="Maroon" title="c2">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="trees_3.html#V3" title="TREES_3:attr.3">constituted-DTrees</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> implies <font color="Maroon" title="c1">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_9.html#K9" title="TREES_9:func.9">Subtrees</a> <font color="Maroon" title="c2">X</font> )</span><br/>



<b>assume </b><a NAME="E1:54"/>
<font color="Maroon" title="c1">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_9.html#K9" title="TREES_9:func.9">Subtrees</a> <font color="Maroon" title="c2">X</font></span><br/>

<b>then reconsider </b><font color="Maroon" title="c3">t</font> = <font color="Maroon" title="c1">t</font> as    <a href="trees_3.html#M3" title="TREES_3:mode.3">Element</a> of <font color="Maroon" title="c2">X</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c4">e</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="trees_4.html#NM1" title="TREES_4:NM.1">Node</a> of <font color="Maroon" title="c3">t</font> <b>by </b><i><a class="ref" href="trees_1.html#T47" title="TREES_1:th.47">TREES_1:47</a></i>;<br/>
<a NAME="E4:54"/>
<font color="Maroon" title="c3">t</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Maroon" title="c4">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">t</font>
 
<b>by </b><i><a class="ref" href="trees_9.html#T1" target="_self" title="TREES_9:th.1">Th1</a></i>;<br/>
<b>hence </b><a NAME="E5:54"/>
<font color="Maroon" title="c1">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_9.html#K9" title="TREES_9:func.9">Subtrees</a> <font color="Maroon" title="c2">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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