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<b>let </b><font color="Maroon">p</font> be   <a href="finseq_1.html#NM1">FinSequence</a>, <font color="Maroon">q</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>

<b>thus </b><a NAME="E1:22"/>
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="trees_1.html#K1" target="_self">ProperPrefixes</a> <font color="Maroon">q</font> implies <font color="Maroon">p</font> <a href="trees_1.html#NR3" target="_self">is_a_proper_prefix_of</a> <font color="Maroon">q</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="trees_1.html#K1" target="_self">ProperPrefixes</a> <font color="Maroon">q</font>
 ;<br/>

<a NAME="E2:22_1"/><b>then </b>
 ex <font color="Olive">r</font> being  <a href="finseq_1.html#NM1">FinSequence</a> st <br/>( <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Olive">r</font> &amp; <font color="Olive">r</font> <a href="trees_1.html#NR3" target="_self">is_a_proper_prefix_of</a> <font color="Maroon">q</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:22_1"/>
<font color="Maroon">p</font> <a href="trees_1.html#NR3" target="_self">is_a_proper_prefix_of</a> <font color="Maroon">q</font>
 ;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:22"/>
( <font color="Maroon">p</font> <a href="trees_1.html#NR3" target="_self">is_a_proper_prefix_of</a> <font color="Maroon">q</font> implies <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="trees_1.html#K1" target="_self">ProperPrefixes</a> <font color="Maroon">q</font> )
 <b>by </b><i/>;<br/>


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