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<b>let </b><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font>, <font color="Maroon" title="c3">r</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>;<br/>

<b>assume </b><a NAME="E1:24"/>
<font color="Maroon" title="c2">q</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">r</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="c1">p</font>
 ;<br/>

<a NAME="E2:24"/><b>then </b>
( <font color="Maroon" title="c2">q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Maroon" title="c2">q</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">r</font> &amp; <font color="Maroon" title="c2">q</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">r</font> <a href="trees_1.html#NR3" title="TREES_1:NR.3">is_a_proper_prefix_of</a> <font color="Maroon" title="c1">p</font> )
 
<b>by </b><i><a class="ref" href="trees_1.html#T8" target="_self" title="TREES_1:th.8">Th8</a>, <a class="ref" href="trees_1.html#T36" target="_self" title="TREES_1:th.36">Th36</a></i>;<br/>
<a NAME="E3:24"/><b>then </b>
<font color="Maroon" title="c2">q</font> <a href="trees_1.html#NR3" title="TREES_1:NR.3">is_a_proper_prefix_of</a> <font color="Maroon" title="c1">p</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T59" title="XBOOLE_1:th.59">XBOOLE_1:59</a></i>;<br/>
<b>hence </b><a NAME="E4:24"/>
<font color="Maroon" title="c2">q</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="c1">p</font>
 <b>by </b><i><a class="ref" href="trees_1.html#T36" target="_self" title="TREES_1:th.36">Th36</a></i>;<br/>


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