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<b>let </b><font color="Maroon" title="c1">W</font> be   <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a>;<br/><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c4">B</font> be   <a href="trees_2.html#NM3" title="TREES_2:NM.3">Branch</a> of <font color="Maroon" title="c1">W</font>;<br/>







<b>assume </b><a NAME="E1:39"/>
<font color="Maroon" title="c2">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Maroon" title="c3">q</font>
 ;<br/>

<a NAME="E2:39"/><b>then </b>
( <font color="Maroon" title="c2">p</font> <a href="trees_1.html#NR3" title="TREES_1:NR.3">is_a_proper_prefix_of</a> <font color="Maroon" title="c3">q</font> or <font color="Maroon" title="c2">p</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c3">q</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D8" title="XBOOLE_0:def.8">XBOOLE_0:def 8</a></i>;<br/>
<a NAME="E3:39"/><b>then </b><i><font color="Green" title="E19">A1</font></i>: 
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_1.html#K1" title="TREES_1:func.1">ProperPrefixes</a> <font color="Maroon" title="c3">q</font> or <font color="Maroon" title="c2">p</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c3">q</font> )
 
<b>by </b><i><a class="ref" href="trees_1.html#D4" title="TREES_1:def.4">TREES_1:def 4</a></i>;<br/>
<b>assume </b><a NAME="E4:39"/><i><font color="Green" title="E20">A2</font></i>: 
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">B</font>
 ;<br/>

<a NAME="E5:39"/><b>then </b>
 <a href="trees_1.html#K1" title="TREES_1:func.1">ProperPrefixes</a> <font color="Maroon" title="c3">q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B</font>
 
<b>by </b><i><a class="ref" href="trees_2.html#D7" target="_self" title="TREES_2:def.7">Def7</a></i>;<br/>
<b>hence </b><a NAME="E6:39"/>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">B</font>
 <b>by </b><i><a class="txt" href="trees_2.html#E3:39"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="trees_2.html#E4:39"><i><font color="Green" title="E20">A2</font></i></a></i>;<br/>


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