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<b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:23"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> &amp; 2 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">n</font> &amp; <font color="Maroon">f</font> <a href="topreal1.html#NR2" target="_self">is_S-Seq</a>  )
 ;<br/>

<b>then reconsider </b><font color="Maroon">f'</font> = <font color="Maroon">f</font> as  <a href="funct_1.html#V2">one-to-one</a> <a href="topreal1.html#V1">special</a> <a href="topreal1.html#V2">unfolded</a> <a href="topreal1.html#V3">s.n.c.</a> <a href="struct_0.html#NM7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <b>by </b><i><a class="ref" href="topreal1.html#D10">TOPREAL1:def 10</a></i>;<br/>
<a NAME="E3:23"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="ref" href="jordan3.html#T1" target="_self">Th1</a>, <a class="ref" href="rfinseq.html#D2">RFINSEQ:def 2</a></i>;<br/>
<a NAME="E4:23"/><b>then </b>
( <font color="Maroon">f'</font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">n</font> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f'</font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2 &amp; <font color="Maroon">f'</font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">n</font> is <a href="topreal1.html#V2">unfolded</a> &amp; <font color="Maroon">f'</font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">n</font> is <a href="topreal1.html#V3">s.n.c.</a> &amp; <font color="Maroon">f'</font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">n</font> is <a href="topreal1.html#V1">special</a> )
 
<b>by </b><i><a class="ref" href="jordan3.html#T1" target="_self">Th1</a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/>
<b>hence </b><a NAME="E5:23"/>
<font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">n</font> <a href="topreal1.html#NR2" target="_self">is_S-Seq</a> 
 <b>by </b><i><a class="ref" href="topreal1.html#D10">TOPREAL1:def 10</a></i>;<br/>


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