<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="topreal2.html#NM1">Simple_closed_curve</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="jordan_a.html#M1" target="_self">Segmentation</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:33"/><i><font color="Green">E25</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:33"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E3:33"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E4:33"/><i><font color="Green">E28</font></i>: 
not <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="gobrd10.html#R1">are_adjacent1</a> 
 ;<br/>

<a NAME="E5:33"/>
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="jordan_a.html#E2:33"><i><font color="Green">E26</font></i></a>, <a class="txt" href="jordan_a.html#E3:33"><i><font color="Green">E27</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E6:33"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="jordan_a.html#K2" target="_self">Segm</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="jordan7.html#K1">Segment</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="jordan_a.html#E1:33"><i><font color="Green">E25</font></i></a>, <a class="ref" href="jordan_a.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E7:33"/>
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="jordan_a.html#E1:33"><i><font color="Green">E25</font></i></a>, <a class="txt" href="jordan_a.html#E2:33"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E8:33"/><b>then </b>
 <a href="jordan_a.html#K2" target="_self">Segm</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="jordan7.html#K1">Segment</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="jordan_a.html#E3:33"><i><font color="Green">E27</font></i></a>, <a class="ref" href="jordan_a.html#D4" target="_self">Def4</a></i>;<br/>
<b>hence </b><a NAME="E9:33"/>
 <a href="jordan_a.html#K2" target="_self">Segm</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#R1">misses</a>  <a href="jordan_a.html#K2" target="_self">Segm</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="jordan_a.html#E1:33"><i><font color="Green">E25</font></i></a>, <a class="txt" href="jordan_a.html#E2:33"><i><font color="Green">E26</font></i></a>, <a class="txt" href="jordan_a.html#E3:33"><i><font color="Green">E27</font></i></a>, <a class="txt" href="jordan_a.html#E4:33"><i><font color="Green">E28</font></i></a>, <a class="txt" href="jordan_a.html#E6:33"><i><font color="Green">E29</font></i></a>, <a class="ref" href="jordan_a.html#D3" target="_self">Def3</a></i>;<br/>


</div>
