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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></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> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:133"/>
<font color="Maroon">c<sub>3</sub></font> <a href="jordan2c.html#R2" target="_self">is_outside_component_of</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span><b> such that </b><br/><a NAME="E3:133"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E4:133"/><i><font color="Green">E116</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="connsp_1.html#R3">is_a_component_of</a> <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span>
 <b>and </b><br/><a NAME="E5:133"/>
<font color="Maroon">c<sub>4</sub></font> is  not  <a href="tbsp_1.html#V6">bounded</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14">Euclid</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="jordan2c.html#T18" target="_self">Th18</a></i>;<br/>
<a NAME="E6:133"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="connsp_1.html#V2">connected</a>
 
<b>by </b><i><a class="txt" href="jordan2c.html#E4:133"><i><font color="Green">E116</font></i></a>, <a class="ref" href="connsp_1.html#D5">CONNSP_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E7:133"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="txt" href="jordan2c.html#E3:133"><i><font color="Green">E115</font></i></a>, <a class="ref" href="connsp_1.html#T24">CONNSP_1:24</a></i>;<br/>


</div>
