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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">v1</font>, <font color="Maroon" title="c3">v2</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>;<br/><b>let </b><font color="Maroon" title="c4">C</font> be    <a href="trees_2.html#M1" title="TREES_2:mode.1">Chain</a> of <font color="Maroon" title="c1">W</font>;<br/>







<b>assume </b><a NAME="E1:35"/><i><font color="Green" title="E16">A1</font></i>: 
( <font color="Maroon" title="c2">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font> &amp; <font color="Maroon" title="c3">v2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c5">p</font> = <font color="Maroon" title="c2">v1</font>, <font color="Maroon" title="c6">q</font> = <font color="Maroon" title="c3">v2</font> as    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of <font color="Maroon" title="c1">W</font> ;<br/>
<b>assume </b><a NAME="E3:35"/>
not <font color="Maroon" title="c2">v1</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">v2</font>
 ;<br/>

<a NAME="E4:35"/><b>then </b>
( <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c6">q</font> <a href="xboole_0.html#R3" title="XBOOLE_0:pred.3">are_c=-comparable</a>  &amp; not <font color="Maroon" title="c2">v1</font> <a href="trees_1.html#NR3" title="TREES_1:NR.3">is_a_proper_prefix_of</a> <font color="Maroon" title="c3">v2</font> )
 
<b>by </b><i><a class="txt" href="trees_2.html#E1:35"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="trees_2.html#D3" target="_self" title="TREES_2:def.3">Def3</a>, <a class="ref" href="trees_1.html#T36" title="TREES_1:th.36">TREES_1:36</a></i>;<br/>
<a NAME="E5:35"/><b>then </b>
( ( <font color="Maroon" title="c2">v1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Maroon" title="c3">v2</font> or <font color="Maroon" title="c3">v2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Maroon" title="c2">v1</font> ) &amp; (  not <font color="Maroon" title="c2">v1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Maroon" title="c3">v2</font> or <font color="Maroon" title="c2">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v2</font> ) )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D8" title="XBOOLE_0:def.8">XBOOLE_0:def 8</a>, <a class="ref" href="xboole_0.html#D9" title="XBOOLE_0:def.9">XBOOLE_0:def 9</a></i>;<br/>
<b>hence </b><a NAME="E6:35"/>
<font color="Maroon" title="c3">v2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Maroon" title="c2">v1</font>
 ;<br/>


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