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

<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">V</font> be   <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> <font color="Maroon" title="c1">n</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c3">s1</font>, <font color="Maroon" title="c4">s2</font>, <font color="Maroon" title="c5">t1</font>, <font color="Maroon" title="c6">t2</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> <font color="Maroon" title="c1">n</font></span>)</span>;<br/>











<b>assume </b><a NAME="E1:28"/><i><font color="Green" title="E20">A1</font></i>: 
for <font color="Olive" title="b1">A</font> being  <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> <font color="Maroon" title="c1">n</font></span>)</span>  st <font color="Olive" title="b1">A</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c4">s2</font> &amp; <font color="Olive" title="b1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">V</font> holds <br/><font color="Olive" title="b1">A</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c5">t1</font>,<font color="Maroon" title="c6">t2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="jordan18.html#D3" target="_self" title="JORDAN18:def.3">JORDAN18:def 3</a><br/>

<b>let </b><font color="Maroon" title="c7">A</font> be   <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> <font color="Maroon" title="c1">n</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="jordan18.html#D3" target="_self" title="JORDAN18:def.3">JORDAN18:def 3</a><br/>

<b>assume </b><b>that </b><br/><a NAME="E2:28"/><i><font color="Green" title="E21">A2</font></i>: 
<font color="Maroon" title="c7">A</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c3">s1</font>
 <b>and </b><br/><a NAME="E3:28"/><i><font color="Green" title="E22">A3</font></i>: 
<font color="Maroon" title="c7">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">V</font>
 ;<br/>

<a NAME="E4:28"/>
<font color="Maroon" title="c7">A</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c4">s2</font>
 
<b>by </b><i><a class="txt" href="jordan18.html#E2:28"><i><font color="Green" title="E21">A2</font></i></a>, <a class="ref" href="jordan5b.html#T14" title="JORDAN5B:th.14">JORDAN5B:14</a></i>;<br/>
<b>hence </b><a NAME="E5:28"/>
<font color="Maroon" title="c7">A</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c5">t1</font>,<font color="Maroon" title="c6">t2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="txt" href="jordan18.html#E1:28"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="jordan18.html#E3:28"><i><font color="Green" title="E22">A3</font></i></a></i>;<br/>


</div>
