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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>

<b>assume </b><a NAME="E1:1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">is_a_prefix_of</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:1"/><b>then </b><i><font color="Green">E2</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being  <a href="finseq_1.html#NM1">FinSequence</a> st <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="finseq_1.html#K7">^</a> <font color="Olive">b<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="trees_1.html#T8">TREES_1:8</a></i>;<br/>
<b>assume </b><a NAME="E3:1"/>
<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="E4:1"/><b>then </b><i><font color="Green">E3</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being  <a href="finseq_1.html#NM1">FinSequence</a> st <font color="Maroon">c<sub>3</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="Olive">b<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="trees_1.html#T8">TREES_1:8</a></i>;<br/>
<a NAME="E5:1"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> or  <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>1</sub></font> )
 
;<br/>
<a NAME="E6:1"/><b>then </b>
( ex <font color="Olive">b<sub>1</sub></font> being  <a href="finseq_1.html#NM1">FinSequence</a> st <font color="Maroon">c<sub>1</sub></font> <a href="finseq_1.html#K7">^</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> or ex <font color="Olive">b<sub>1</sub></font> being  <a href="finseq_1.html#NM1">FinSequence</a> st <font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K7">^</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="trees_2.html#E2:1"><i><font color="Green">E2</font></i></a>, <a class="txt" href="trees_2.html#E4:1"><i><font color="Green">E3</font></i></a>, <a class="ref" href="finseq_1.html#T64">FINSEQ_1:64</a></i>;<br/>
<b>hence </b><a NAME="E7:1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">is_a_prefix_of</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">is_a_prefix_of</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="trees_1.html#T8">TREES_1:8</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D9">XBOOLE_0:def 9</a><br/>


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