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<b>let </b><font color="Maroon">W</font> be   <a href="trees_1.html#NM1">Tree</a>;<br/><b>let </b><font color="Maroon">p</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">q</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">B</font> be   <a href="trees_2.html#NM3">Branch</a> of <font color="Maroon">W</font>;<br/>







<b>assume </b><a NAME="E1:40"/>
<font color="Maroon">p</font> <a href="tarski.html#R1">is_a_prefix_of</a> <font color="Maroon">q</font>
 ;<br/>

<a NAME="E2:40"/><b>then </b>
( <font color="Maroon">p</font> <a href="trees_1.html#NR3" target="_self">is_a_proper_prefix_of</a> <font color="Maroon">q</font> or <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D8">XBOOLE_0:def 8</a></i>;<br/>
<a NAME="E3:40"/><b>then </b><i><font color="Green">E50</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="trees_1.html#K1">ProperPrefixes</a> <font color="Maroon">q</font> or <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> )
 
<b>by </b><i><a class="ref" href="trees_1.html#D4">TREES_1:def 4</a></i>;<br/>
<b>assume </b><a NAME="E4:40"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 ;<br/>

<a NAME="E5:40"/><b>then </b>
 <a href="trees_1.html#K1">ProperPrefixes</a> <font color="Maroon">q</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:40"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 <b>by </b><i>, </i>;<br/>


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