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

<b>let </b><font color="Maroon" title="c1">C</font> be  <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">p</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>  st  <a href="topreal1.html#K7" title="TOPREAL1:func.7">east_halfline</a> <font color="Olive" title="b1">p</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c1">C</font> holds <br/> <a href="topreal1.html#K7" title="TOPREAL1:func.7">east_halfline</a> <font color="Olive" title="b1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="jordan2c.html#K2" title="JORDAN2C:func.2">UBD</a> <font color="Maroon" title="c1">C</font></span><br/><b>let </b><font color="Maroon" title="c2">p</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="topreal1.html#K7" title="TOPREAL1:func.7">east_halfline</a> <font color="Maroon" title="c2">p</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c1">C</font> implies  <a href="topreal1.html#K7" title="TOPREAL1:func.7">east_halfline</a> <font color="Maroon" title="c2">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="jordan2c.html#K2" title="JORDAN2C:func.2">UBD</a> <font color="Maroon" title="c1">C</font> )</span><br/>



<b>set </b><font color="Maroon" title="c3">WH</font> =  <a href="topreal1.html#K7" title="TOPREAL1:func.7">east_halfline</a> <font color="Maroon" title="c2">p</font>;<br/>
<a NAME="E1:142"/><i><font color="Green" title="E113">A1</font></i>: 
( not  <a href="topreal1.html#K7" title="TOPREAL1:func.7">east_halfline</a> <font color="Maroon" title="c2">p</font> is <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a> &amp; not  <a href="topreal1.html#K7" title="TOPREAL1:func.7">east_halfline</a> <font color="Maroon" title="c2">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="topreal1.html#K7" title="TOPREAL1:func.7">east_halfline</a> <font color="Maroon" title="c2">p</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> )
 
<b>by </b><i><a class="ref" href="jordan2c.html#T129" target="_self" title="JORDAN2C:th.129">Th129</a></i>;<br/>
<b>assume </b><a NAME="E2:142"/>
 <a href="topreal1.html#K7" title="TOPREAL1:func.7">east_halfline</a> <font color="Maroon" title="c2">p</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c1">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="topreal1.html#K7" title="TOPREAL1:func.7">east_halfline</a> <font color="Maroon" title="c2">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="jordan2c.html#K2" title="JORDAN2C:func.2">UBD</a> <font color="Maroon" title="c1">C</font></span><br/>

<b>hence </b><a NAME="E3:142"/>
 <a href="topreal1.html#K7" title="TOPREAL1:func.7">east_halfline</a> <font color="Maroon" title="c2">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="jordan2c.html#K2" title="JORDAN2C:func.2">UBD</a> <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="jordan2c.html#E1:142"><i><font color="Green" title="E113">A1</font></i></a>, <a class="ref" href="jordan2c.html#T133" target="_self" title="JORDAN2C:th.133">Th133</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
