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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="sppol_2.html#NM1">S-Sequence_in_R2</a>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:76"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E2:76"/><i><font color="Green">E63</font></i>: 
not <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="finseq_5.html#K5">Ins</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/>
<b>thus </b><a NAME="E3:76"/>
 <a href="finseq_5.html#K5">Ins</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 <b>by </b><i><a class="txt" href="sppol_2.html#E2:76"><i><font color="Green">E63</font></i></a>, <a class="ref" href="finseq_5.html#T79">FINSEQ_5:79</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="topreal1.html#D10">TOPREAL1:def 10</a><br/>

<a NAME="E4:76"/><i><font color="Green">E64</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2
 
<b>by </b><i><a class="ref" href="topreal1.html#D10">TOPREAL1:def 10</a></i>;<br/>
<a NAME="E5:76"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K5">Ins</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></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">c<sub>3</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="finseq_5.html#T72">FINSEQ_5:72</a></i>;<br/>
<a NAME="E6:76"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K5">Ins</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<b>hence </b><a NAME="E7:76"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K5">Ins</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2
 <b>by </b><i><a class="txt" href="sppol_2.html#E4:76"><i><font color="Green">E64</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>

<b>thus </b><a NAME="E8:76"/>
 <a href="finseq_5.html#K5">Ins</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> is <a href="topreal1.html#V2">unfolded</a>
 <b>by </b><i><a class="txt" href="sppol_2.html#E1:76"><i><font color="Green">E62</font></i></a>, <a class="ref" href="sppol_2.html#T33" target="_self">Th33</a></i>;<br/>

<b>thus </b><a NAME="E9:76"/>
 <a href="finseq_5.html#K5">Ins</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> is <a href="topreal1.html#V3">s.n.c.</a>
 <b>by </b><i><a class="txt" href="sppol_2.html#E1:76"><i><font color="Green">E62</font></i></a>, <a class="txt" href="sppol_2.html#E2:76"><i><font color="Green">E63</font></i></a>, <a class="ref" href="sppol_2.html#T38" target="_self">Th38</a></i>;<br/>

<b>thus </b><a NAME="E10:76"/>
 <a href="finseq_5.html#K5">Ins</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> is <a href="topreal1.html#V1">special</a>
 <b>by </b><i><a class="txt" href="sppol_2.html#E1:76"><i><font color="Green">E62</font></i></a>, <a class="ref" href="sppol_2.html#T44" target="_self">Th44</a></i>;<br/>


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