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<b>let </b><font color="Maroon">P</font> be   <a href="struct_0.html#NM2">Subset</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">p1</font> be   <a href="pre_topc.html#NM2">Point</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">p2</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>





<b>given </b><font color="Maroon">f</font> being   <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> such that </b><a NAME="E1:78"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">f</font> <a href="topreal1.html#NR2" target="_self">is_S-Seq</a> 
 <b>and </b><br/><a NAME="E2:78"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">P</font> <a href="hidden.html#R1">=</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E3:78"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">p1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> 1 &amp; <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="topreal4.html#D1">TOPREAL4:def 1</a><br/>

<b>take </b><font color="Maroon">g</font> =  <a href="finseq_5.html#K4">Rev</a> <font color="Maroon">f</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="topreal4.html#D1">TOPREAL4:def 1</a><br/>

<b>thus </b><a NAME="E4:78"/>
( <font color="Maroon">g</font> <a href="topreal1.html#NR2" target="_self">is_S-Seq</a>  &amp; <font color="Maroon">P</font> <a href="hidden.html#R1">=</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">g</font> )
 <b>by </b><i><a class="ref" href="sppol_2.html#T12" target="_self">Th12</a>, <a class="ref" href="sppol_2.html#T13" target="_self">Th13</a>, , <a class="ref" href="sppol_2.html#T7" target="_self">Th7</a></i>;<br/>

<a NAME="E5:78"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="sppol_2.html#T12" target="_self">Th12</a>, <a class="ref" href="topreal1.html#D10">TOPREAL1:def 10</a></i>;<br/>
<a NAME="E6:78"/><b>then </b>
( not <font color="Maroon">f</font> is <a href="xboole_0.html#V1">empty</a> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a>, <a class="ref" href="finseq_5.html#D3">FINSEQ_5:def 3</a></i>;<br/>
<b>hence </b><a NAME="E7:78"/>
( <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="finseq_4.html#K4">/.</a> 1 &amp; <font color="Maroon">p1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">g</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="finseq_5.html#T68">FINSEQ_5:68</a></i>;<br/>


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