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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/>



<a NAME="E1:42"/><i><font color="Green">E17</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</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="binarith.html#D3">BINARITH:def 3</a></i>;<br/>
1 <a href="binarith.html#K3">-'</a> 1 = 
<span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> 1

<br/>.= 
0
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
;<br/>
<a NAME="E3:42"/><b>then </b>
<font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p1">(<span class="default">1 <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="finseq_5.html#T31">FINSEQ_5:31</a></i>;<br/>
<a NAME="E4:42"/><b>then </b><i><font color="Green">E18</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; <font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p1">(<span class="default">1 <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="finseq_8.html#NR3" target="_self">is_preposition_of</a>  )
 
;<br/>
<a NAME="E5:42"/>
for <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp; <font color="Olive">j</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p1">(<span class="default"><font color="Olive">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="finseq_8.html#NR3" target="_self">is_preposition_of</a>  holds <br/><font color="Olive">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 
;<br/>
<a NAME="E6:42"/><b>then </b>
 <a href="finseq_8.html#K7" target="_self">instr</a> 1,<font color="Maroon">f</font>,<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</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="finseq_8.html#T4" target="_self">Th4</a>, </i>;<br/>
<b>hence </b><a NAME="E7:42"/>
<font color="Maroon">f</font> <a href="finseq_8.html#R5" target="_self">is_terminated_by</a> <font color="Maroon">f</font>
 <b>by </b><i/>;<br/>


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