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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="compts_1.html#V6">compact</a> <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">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>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="topreal1.html#K6">north_halfline</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<a NAME="E1:150"/><i><font color="Green">E122</font></i>: 
( not  <a href="topreal1.html#K6">north_halfline</a> <font color="Maroon">c<sub>2</sub></font> is <a href="jordan2c.html#V1" target="_self">Bounded</a> &amp; not  <a href="topreal1.html#K6">north_halfline</a> <font color="Maroon">c<sub>2</sub></font> is <a href="xboole_0.html#V1">empty</a> &amp;  <a href="topreal1.html#K6">north_halfline</a> <font color="Maroon">c<sub>2</sub></font> is <a href="connsp_1.html#V2">connected</a> )
 
<b>by </b><i><a class="ref" href="jordan2c.html#T130" target="_self">Th130</a></i>;<br/>
<b>assume </b><a NAME="E2:150"/>
 <a href="topreal1.html#K6">north_halfline</a> <font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>hence </b><a NAME="E3:150"/>
 <a href="topreal1.html#K6">north_halfline</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="jordan2c.html#K2" target="_self">UBD</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="jordan2c.html#E1:150"><i><font color="Green">E122</font></i></a>, <a class="ref" href="jordan2c.html#T133" target="_self">Th133</a></i>;<br/>


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