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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">V</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">n</font></span>)</span>;<br/><b>let </b><font color="Maroon">s1</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> <font color="Maroon">n</font></span>)</span>;<br/><b>let </b><font color="Maroon">s2</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> <font color="Maroon">n</font></span>)</span>;<br/><b>let </b><font color="Maroon">t1</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> <font color="Maroon">n</font></span>)</span>;<br/><b>let </b><font color="Maroon">t2</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> <font color="Maroon">n</font></span>)</span>;<br/>











<b>assume </b><a NAME="E1:28"/><i><font color="Green">E55</font></i>: 
for <font color="Olive">A</font> being  <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">n</font></span>)</span>  st <font color="Olive">A</font> <a href="topreal1.html#R1">is_an_arc_of</a> <font color="Maroon">s1</font>,<font color="Maroon">s2</font> &amp; <font color="Olive">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V</font> holds <br/><font color="Olive">A</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">t1</font>,<font color="Maroon">t2</font></span><a href="tarski.html#K2">}</a></span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="jordan18.html#D3" target="_self">JORDAN18:def 3</a><br/>

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

<b>assume </b><b>that </b><br/><a NAME="E2:28"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">A</font> <a href="topreal1.html#R1">is_an_arc_of</a> <font color="Maroon">s2</font>,<font color="Maroon">s1</font>
 <b>and </b><br/><a NAME="E3:28"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V</font>
 ;<br/>

<a NAME="E4:28"/>
<font color="Maroon">A</font> <a href="topreal1.html#R1">is_an_arc_of</a> <font color="Maroon">s1</font>,<font color="Maroon">s2</font>
 
<b>by </b><i>, <a class="ref" href="jordan5b.html#T14">JORDAN5B:14</a></i>;<br/>
<b>hence </b><a NAME="E5:28"/>
<font color="Maroon">A</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">t1</font>,<font color="Maroon">t2</font></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i>, </i>;<br/>


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