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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="topreal2.html#NM1">Simple_closed_curve</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</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>assume </b><b>that </b><br/><a NAME="E1:18"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="topreal1.html#R1">is_an_arc_of</a>  <a href="pscomp_1.html#K27">W-min</a> <font color="Maroon">c<sub>1</sub></font>, <a href="pscomp_1.html#K31">E-max</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E2:18"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E3:18"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="compts_1.html#V6">compact</a>
 
<b>by </b><i><a class="txt" href="jordan16.html#E1:18"><i><font color="Green">E12</font></i></a>, <a class="ref" href="jordan5a.html#T1">JORDAN5A:1</a></i>;<br/>
<b>hence </b><a NAME="E4:18"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="jordan6.html#K9">Lower_Arc</a> <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="jordan16.html#E1:18"><i><font color="Green">E12</font></i></a>, <a class="txt" href="jordan16.html#E2:18"><i><font color="Green">E13</font></i></a>, <a class="ref" href="topmetr3.html#T19">TOPMETR3:19</a></i>;<br/>


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