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<b>let </b><font color="Maroon" title="c1">T</font> be   <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">t</font> being   <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of <font color="Maroon" title="c1">T</font> holds   <a href="trees_1.html#K1" title="TREES_1:func.1">ProperPrefixes</a> <font color="Olive" title="b1">t</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="trees_2.html#M1" title="TREES_2:mode.1">Chain</a> of <font color="Maroon" title="c1">T</font></span><br/><b>let </b><font color="Maroon" title="c2">t</font> be    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="trees_1.html#K1" title="TREES_1:func.1">ProperPrefixes</a> <font color="Maroon" title="c2">t</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="trees_2.html#M1" title="TREES_2:mode.1">Chain</a> of <font color="Maroon" title="c1">T</font></span><br/>



<a NAME="E1:14"/><i><font color="Green" title="E13">A1</font></i>: 
 <a href="trees_1.html#K1" title="TREES_1:func.1">ProperPrefixes</a> <font color="Maroon" title="c2">t</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">T</font>
 
<b>by </b><i><a class="ref" href="trees_1.html#D5" title="TREES_1:def.5">TREES_1:def 5</a></i>;<br/>
<a NAME="E2:14"/>
for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <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>   st <font color="Olive" title="b1">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="c2">t</font> &amp; <font color="Olive" title="b2">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="c2">t</font> holds <br/><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font> <a href="xboole_0.html#R3" title="XBOOLE_0:pred.3">are_c=-comparable</a> 
 
<b>by </b><i><a class="ref" href="trees_1.html#T42" title="TREES_1:th.42">TREES_1:42</a></i>;<br/>
<b>hence </b><a NAME="E3:14"/>
 <a href="trees_1.html#K1" title="TREES_1:func.1">ProperPrefixes</a> <font color="Maroon" title="c2">t</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="trees_2.html#M1" title="TREES_2:mode.1">Chain</a> of <font color="Maroon" title="c1">T</font>
 <b>by </b><i><a class="txt" href="qc_lang4.html#E1:14"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="trees_2.html#D3" title="TREES_2:def.3">TREES_2:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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