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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="trees_1.html#NM1">Tree</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></font> be    <a href="trees_2.html#M1" target="_self">Chain</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><a NAME="E1:42"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> &amp; not <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">is_a_prefix_of</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E2:42"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="trees_1.html#K1">ProperPrefixes</a> <font color="Maroon">c<sub>2</sub></font> &amp; not <font color="Maroon">c<sub>3</sub></font> <a href="trees_1.html#NR3" target="_self">is_a_proper_prefix_of</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="trees_2.html#T23" target="_self">Th23</a>, <a class="ref" href="trees_1.html#T24">TREES_1:24</a></i>;<br/>
<b>hence </b><a NAME="E3:42"/>
contradiction
 <b>by </b><i><a class="ref" href="trees_1.html#T36">TREES_1:36</a></i>;<br/>


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