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<b>let </b><font color="Maroon">n</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">M</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>



<b>assume </b><a NAME="E1:6"/><i><font color="Green">E43</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="xcmplx_0.html#K2">+</a> 1
 ;<br/>

<a NAME="E2:6"/><b>then </b>
<font color="Maroon">M</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/>
<b>then consider </b><font color="Maroon">q</font> being   <a href="finseq_1.html#NM1">FinSequence</a>, <font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:6"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">M</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</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">x</font></span><a href="finseq_1.html#K9">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T63">FINSEQ_1:63</a></i>;<br/>
<b>reconsider </b><font color="Maroon">n</font> = <font color="Maroon">n</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E6:6"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1
 
;<br/>
<i><font color="Green">E52</font></i>:  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">q</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">x</font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span>
<b>by </b><i>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">q</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#T56">FINSEQ_1:56</a></i>
;<br/>
<a NAME="E8:6"/><b>then </b><i><font color="Green">E54</font></i>: 
<font color="Maroon">M</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#T59">FINSEQ_1:59</a></i>;<br/>
<a NAME="E9:6"/><i><font color="Green">E55</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_3.html#K2">Del</a> <font color="Maroon">M</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">q</font>
 
<b>by </b><i>, </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:6_2"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</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">q</font></span>)</span>
 ;<br/><a NAME="E2:6_2"/><b>then </b><i><font color="Green">E58</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E3:6_2"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">q</font> )
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E4:6_2"/><b>then </b>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font> )
 <b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="finseq_3.html#K2">Del</a> <font color="Maroon">M</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<font color="Maroon">M</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, , <a class="ref" href="finseq_3.html#T119">FINSEQ_3:119</a></i>
<br/>.= 
<font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, , <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E11:6"/>
<font color="Maroon">M</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_3.html#K2">Del</a> <font color="Maroon">M</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font></span>)</span></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font></span>)</span></span>)</span></span><a href="finseq_1.html#K9">*&gt;</a></span>
 <b>by </b><i>, , , <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/>


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