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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="struct_0.html#NM8">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">c<sub>2</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>assume </b><b>that </b><br/><a NAME="E1:73"/><i><font color="Green">E64</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="topreal1.html#NR2" target="_self">is_S-Seq</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>and </b><br/><a NAME="E2:73"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font></span>)</span>
 ;<br/>

<a NAME="E3:73"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="jordan3.html#E1:73"><i><font color="Green">E64</font></i></a>, <a class="ref" href="topreal1.html#T28">TOPREAL1:28</a></i>;<br/>
<a NAME="E4:73"/><b>then </b><i><font color="Green">E66</font></i>: 
<font color="Maroon">c<sub>1</sub></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="E5:73"/><i><font color="Green">E67</font></i>: 
(  <a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>1</sub></font> <a href="topreal1.html#NR2" target="_self">is_S-Seq</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K5">L~</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="jordan3.html#E1:73"><i><font color="Green">E64</font></i></a>, <a class="ref" href="sppol_2.html#T22">SPPOL_2:22</a>, <a class="ref" href="sppol_2.html#T47">SPPOL_2:47</a></i>;<br/>
<i><font color="Green">E68</font></i>:  <a href="jordan3.html#K3" target="_self">L_Cut</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> = 
 <a href="jordan3.html#K3" target="_self">L_Cut</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <span class="p2">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="finseq_6.html#T29">FINSEQ_6:29</a></i>
<br/>.= 
 <a href="finseq_5.html#K4">Rev</a> <span class="p1">(<span class="default"><a href="jordan3.html#K4" target="_self">R_Cut</a> <span class="p2">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="jordan3.html#E5:73"><i><font color="Green">E67</font></i></a>, <a class="ref" href="jordan3.html#T57" target="_self">Th57</a></i>
;<br/>
<a NAME="E7:73"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 1
 
<b>by </b><i><a class="txt" href="jordan3.html#E2:73"><i><font color="Green">E65</font></i></a>, <a class="ref" href="finseq_5.html#T65">FINSEQ_5:65</a></i>;<br/>
<a NAME="E8:73"/><b>then </b>
 <a href="jordan3.html#K4" target="_self">R_Cut</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <a href="jordan3.html#R1" target="_self">is_S-Seq_joining</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="jordan3.html#E5:73"><i><font color="Green">E67</font></i></a>, <a class="ref" href="jordan3.html#T67" target="_self">Th67</a></i>;<br/>
<a NAME="E9:73"/><b>then </b>
 <a href="jordan3.html#K3" target="_self">L_Cut</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="jordan3.html#R1" target="_self">is_S-Seq_joining</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1
 
<b>by </b><i><a class="txt" href="jordan3.html#E6:73"><i><font color="Green">E68</font></i></a>, <a class="ref" href="jordan3.html#T48" target="_self">Th48</a></i>;<br/>
<b>hence </b><a NAME="E10:73"/>
 <a href="jordan3.html#K3" target="_self">L_Cut</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="jordan3.html#R1" target="_self">is_S-Seq_joining</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="jordan3.html#E4:73"><i><font color="Green">E66</font></i></a>, <a class="ref" href="finseq_5.html#T68">FINSEQ_5:68</a></i>;<br/>


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