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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   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>assume </b><a NAME="E1:14"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="jordan1h.html#R1">is_sufficiently_large_for</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="jordan13.html#K1">Span</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>
<b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:14"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E3:14"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <span class="p1">(<span class="default"><a href="jordan13.html#K1">Span</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan14.html#E1:14"><i><font color="Green">E11</font></i></a>, <a class="ref" href="jordan14.html#T9" target="_self">Th9</a></i>;<br/>
<a NAME="E4:14"/>
<font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#R1">misses</a>  <a href="goboard9.html#K3">RightComp</a> <span class="p1">(<span class="default"><a href="jordan13.html#K1">Span</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan14.html#E1:14"><i><font color="Green">E11</font></i></a>, <a class="ref" href="jordan14.html#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E5:14"/><b>then </b>
( not <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="goboard9.html#K3">RightComp</a> <span class="p1">(<span class="default"><a href="jordan13.html#K1">Span</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; not <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K5">L~</a> <span class="p1">(<span class="default"><a href="jordan13.html#K1">Span</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="jordan14.html#E2:14"><i><font color="Green">E12</font></i></a>, <a class="txt" href="jordan14.html#E3:14"><i><font color="Green">E13</font></i></a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>
<b>hence </b><a NAME="E6:14"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="goboard9.html#K2">LeftComp</a> <span class="p1">(<span class="default"><a href="jordan13.html#K1">Span</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="jordan14.html#E2:14"><i><font color="Green">E12</font></i></a>, <a class="ref" href="gobrd14.html#T28">GOBRD14:28</a></i>;<br/>


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