<?xml version="1.0"?>
<div class="add">

<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>thus </b><a NAME="E1:8"/>
( <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> implies 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="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> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon">c<sub>3</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><a NAME="E1:8_1"/><i><font color="Green">E6</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_1.html#D1" target="_self">TREES_1:def 1</a><br/>

<b>thus </b><a NAME="E2:8_1"/>
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="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="txt" href="trees_1.html#E1:8_1"><i><font color="Green">E6</font></i></a>, <a class="ref" href="trees_1.html#T3" target="_self">Th3</a></i>;<br/>


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

<b>given </b><font color="Maroon">c<sub>3</sub></font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><a NAME="E2:8"/><i><font color="Green">E6</font></i>: 
<font color="Maroon">c<sub>2</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="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E3:8"/><i><font color="Green">E7</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</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>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E4:8"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="trees_1.html#E2:8"><i><font color="Green">E6</font></i></a>, <a class="ref" href="finseq_1.html#T33">FINSEQ_1:33</a></i>;<br/>
<b>hence </b><a NAME="E5:8"/>
<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>
 <b>by </b><i><a class="txt" href="trees_1.html#E3:8"><i><font color="Green">E7</font></i></a>, <a class="ref" href="trees_1.html#D1" target="_self">Def1</a></i>;<br/>


</div>
