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<b>let </b><font color="Maroon">fs</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/><b>let </b><font color="Maroon">v</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<a NAME="E1:53"/><i><font color="Green">E40</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">v</font></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56">FINSEQ_1:56</a></i>;<br/>
<a NAME="E2:53"/><i><font color="Green">E41</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">v</font></span><a href="finseq_1.html#K9">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56">FINSEQ_1:56</a></i>;<br/>
<a NAME="E3:53"/><i><font color="Green">E48</font></i>: 
 <a href="finseq_3.html#K2">Del</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">v</font></span><a href="finseq_1.html#K9">*&gt;</a></span>,1 <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="53_1"><b>proof </b></a><div class="add">

<a NAME="E1:53_1"/>
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">v</font></span><a href="finseq_1.html#K9">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="wsierp_1.html#E1:53"><i><font color="Green">E40</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E2:53_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_3.html#K2">Del</a> <span class="p3"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">v</font></span><a href="finseq_1.html#K9">*&gt;</a></span>,1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="txt" href="wsierp_1.html#E1:53"><i><font color="Green">E40</font></i></a>, </i>;<br/>
<a NAME="E3:53_1"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_3.html#K2">Del</a> <span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">v</font></span><a href="finseq_1.html#K9">*&gt;</a></span>,1</span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<b>hence </b><a NAME="E4:53_1"/>
 <a href="finseq_3.html#K2">Del</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">v</font></span><a href="finseq_1.html#K9">*&gt;</a></span>,1 <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:53"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">fs</font> <a href="finseq_1.html#K7">^</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">fs</font> &amp; <a href="xboole_0.html#K1">{}</a>  <a href="finseq_1.html#K7">^</a> <font color="Maroon">fs</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fs</font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>;<br/>
<b>hence </b><a NAME="E5:53"/>
 <a href="finseq_3.html#K2">Del</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">v</font></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">fs</font></span>)</span>,1 <a href="hidden.html#R1">=</a> <font color="Maroon">fs</font>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E2:53"><i><font color="Green">E41</font></i></a>, <a class="ref" href="wsierp_1.html#T3" target="_self">Th3</a>, </i>;<br/>

<b>thus </b><a NAME="E6:53"/>
 <a href="finseq_3.html#K2">Del</a> <span class="p1">(<span class="default"><font color="Maroon">fs</font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">v</font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">fs</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">fs</font>
 <b>by </b><i><a class="ref" href="wsierp_1.html#T3" target="_self">Th3</a>, <a class="ref" href="wsierp_1.html#T5" target="_self">Th5</a>, </i>;<br/>


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