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<b>consider </b><font color="Maroon" title="c1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="trees_1.html#K1" title="TREES_1:func.1">ProperPrefixes</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ;<br/>
<b>assume </b><a NAME="E2:23"/><i><font color="Green" title="E18">A1</font></i>: 
not  <a href="trees_1.html#K1" title="TREES_1:func.1">ProperPrefixes</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<b>then reconsider </b><font color="Maroon" title="c2">x</font> = <font color="Maroon" title="c1">x</font> as   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> <b>by </b><i><a class="ref" href="trees_1.html#T35" target="_self" title="TREES_1:th.35">Th35</a></i>;<br/>
<a NAME="E4:23"/>
<font color="Maroon" title="c2">x</font> <a href="trees_1.html#NR3" title="TREES_1:NR.3">is_a_proper_prefix_of</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="txt" href="trees_1.html#E2:23"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="trees_1.html#T36" target="_self" title="TREES_1:th.36">Th36</a></i>;<br/>
<b>hence </b><a NAME="E5:23"/>
contradiction
 <b>by </b><i><a class="ref" href="xboole_1.html#T115" title="XBOOLE_1:th.115">XBOOLE_1:115</a></i>; <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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