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<b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">f</font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>;<br/>



<b>assume </b><a NAME="E1:27"/><i><font color="Green">E17</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 ;<br/>

<span class="p1">(<span class="default">1 <a href="binarith.html#K3">-'</a> 1</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">f</font></span>)</span> = 
0 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span>
<b>by </b><i><a class="ref" href="nat_2.html#T10">NAT_2:10</a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>

;<br/>
<a NAME="E3:27"/><b>then </b>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> &amp;  <a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,1,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> )
 
<b>by </b><i>, <a class="ref" href="jordan3.html#T29">JORDAN3:29</a></i>;<br/>
<b>hence </b><a NAME="E4:27"/>
<font color="Maroon">f</font> <a href="finseq_8.html#R2" target="_self">is_substring_of</a> <font color="Maroon">f</font>,1
 <b>by </b><i/>;<br/>


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