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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>



<b>assume </b><a NAME="E1:19"/>
(  <a href="xboole_0.html#K1">{}</a>  <a href="trees_1.html#NR3" target="_self">is_a_proper_prefix_of</a> <font color="Maroon">c<sub>1</sub></font> or  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<a NAME="E2:19"/><b>then </b><i><font color="Green">E13</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/>
<b>thus </b><a NAME="E3:19"/>
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">is_a_prefix_of</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="trees_1.html#T8" target="_self">Th8</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D8">XBOOLE_0:def 8</a><br/>

<b>assume </b><a NAME="E4:19"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E5:19"/><b>then </b>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 0 <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>;<br/>
<b>hence </b><a NAME="E6:19"/>
contradiction
 <b>by </b><i><a class="txt" href="trees_1.html#E2:19"><i><font color="Green">E13</font></i></a></i>;<br/>


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