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<b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">fs</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>



<b>assume </b><a NAME="E1:46"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">fs</font>
 ;<br/>

<a NAME="E2:46"/><b>then </b>
( <font color="Maroon">a</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp; <font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">fs</font> )
 
<b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">b</font> = <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">fs</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font>, <font color="Maroon">d</font> = <font color="Maroon">a</font> <a href="real_1.html#K5">-</a> 1 as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="int_1.html#T18">INT_1:18</a></i>;<br/>
<a NAME="E4:46"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">fs</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">b</font>
 
;<br/>
<b>then consider </b><font color="Maroon">fs3</font> being   <a href="finseq_1.html#NM1">FinSequence</a>, <font color="Maroon">fs2</font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><br/><a NAME="E6:46"/><i><font color="Green">E41</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">fs3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">fs2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">fs</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fs3</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">fs2</font> )
 <b>by </b><i><a class="ref" href="finseq_2.html#T25">FINSEQ_2:25</a></i>;<br/>
<a NAME="E7:46"/>
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E8:46"/><b>then </b>
<font color="Maroon">fs3</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</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/>
<a NAME="E9:46"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">fs3</font>
 
<b>by </b><i>, <a class="ref" href="finseq_5.html#T6">FINSEQ_5:6</a></i>;<br/>
<a NAME="E10:46"/><b>then </b><i><font color="Green">E48</font></i>: 
<font color="Maroon">fs3</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fs</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>;<br/>
<a NAME="E11:46"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> <a href="nat_1.html#K1">+</a> 1
 
;<br/>
<b>then consider </b><font color="Maroon">fs1</font> being   <a href="finseq_1.html#NM1">FinSequence</a>, <font color="Maroon">v</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E13:46"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">fs3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fs1</font> <a href="finseq_1.html#K7">^</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_2.html#T21">FINSEQ_2:21</a></i>;<br/>
<a NAME="E14:46"/><i><font color="Green">E50</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">fs1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i>, , <a class="ref" href="finseq_2.html#T19">FINSEQ_2:19</a></i>;<br/>
<a NAME="E15:46"/><b>then </b><i><font color="Green">E102</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">fs1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 
;<br/>
<a NAME="E16:46"/>
<font color="Maroon">fs</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font>
 
<b>by </b><i>, , <a class="ref" href="wsierp_1.html#T2" target="_self">Th2</a>, <a class="ref" href="finseq_1.html#T59">FINSEQ_1:59</a></i>;<br/>
<b>hence </b><a NAME="E17:46"/>
 ex <font color="Olive">fs1</font>, <font color="Olive">fs2</font> being  <a href="finseq_1.html#NM1">FinSequence</a> st <br/>( <font color="Maroon">fs</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">fs1</font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">fs</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font></span>)</span></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K7">^</a> <font color="Olive">fs2</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Olive">fs1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="real_1.html#K5">-</a> 1 &amp;  <a href="finseq_1.html#K3">len</a> <font color="Olive">fs2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">fs</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font> )
 <b>by </b><i>, , <a class="txt" href="wsierp_1.html#E1:46"><i><font color="Green">E40</font></i></a></i>;<br/>


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