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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> be    <a href="trees_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:14"/><i><font color="Green">E13</font></i>: 
 <a href="trees_1.html#K1">ProperPrefixes</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="trees_1.html#D5">TREES_1:def 5</a></i>;<br/>
<a NAME="E2:14"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a>  st <font color="Olive">b<sub>1</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; <font color="Olive">b<sub>2</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> holds <br/><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="xboole_0.html#R3">are_c=-comparable</a> 
 
<b>by </b><i><a class="ref" href="trees_1.html#T42">TREES_1:42</a></i>;<br/>
<b>hence </b><a NAME="E3:14"/>
 <a href="trees_1.html#K1">ProperPrefixes</a> <font color="Maroon">c<sub>2</sub></font> is  <a href="finset_1.html#V1">finite</a>  <a href="trees_2.html#M1">Chain</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="qc_lang4.html#E1:14"><i><font color="Green">E13</font></i></a>, <a class="ref" href="trees_2.html#D3">TREES_2:def 3</a></i>;<br/>


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