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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="sppol_2.html#NM2">Special_polygon_in_R2</a>;<br/>

<b>consider </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> being   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></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> 2</span>)</span><b> such that </b><br/><a NAME="E2:97"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>and </b><br/><a NAME="E3:97"/><i><font color="Green">E74</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="topreal4.html#R1">is_S-P_arc_joining</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="topreal4.html#R1">is_S-P_arc_joining</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 <b>and </b><br/><a NAME="E4:97"/>
<font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K2">}</a></span>
 <b>and </b><br/><a NAME="E5:97"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="topreal4.html#D2">TOPREAL4:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>5</sub></font> as   <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/>
<a NAME="E7:97"/>
( <font color="Maroon">c<sub>6</sub></font> is <a href="topreal1.html#V5">being_S-P_arc</a> &amp; <font color="Maroon">c<sub>7</sub></font> is <a href="topreal1.html#V5">being_S-P_arc</a> )
 
<b>by </b><i><a class="txt" href="sppol_2.html#E3:97"><i><font color="Green">E74</font></i></a>, <a class="ref" href="topreal4.html#T2">TOPREAL4:2</a></i>;<br/>
<a NAME="E8:97"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> is <a href="compts_1.html#V6">compact</a> &amp; <font color="Maroon">c<sub>7</sub></font> is <a href="compts_1.html#V6">compact</a> )
 
<b>by </b><i><a class="ref" href="sppol_2.html#T62" target="_self">Th62</a></i>;<br/>
<b>hence </b><a NAME="E9:97"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="compts_1.html#V6">compact</a>
 <b>by </b><i><a class="txt" href="sppol_2.html#E5:97"><i><font color="Green">E75</font></i></a>, <a class="ref" href="compts_1.html#T19">COMPTS_1:19</a></i>;<br/>


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