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<b>consider </b><font color="Maroon">x</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="trees_1.html#K1" target="_self">ProperPrefixes</a> <a href="xboole_0.html#K1">{}</a> ;<br/>
<b>assume </b><a NAME="E2:25"/><i><font color="Green">E28</font></i>: 
not  <a href="trees_1.html#K1" target="_self">ProperPrefixes</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>then reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as   <a href="finseq_1.html#NM1">FinSequence</a> <b>by </b><i/>;<br/>
<a NAME="E4:25"/>
<font color="Maroon">x</font> <a href="trees_1.html#NR3" target="_self">is_a_proper_prefix_of</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:25"/>
contradiction
 <b>by </b><i><a class="ref" href="xboole_1.html#T115">XBOOLE_1:115</a></i>;<br/>


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