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<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="sppol_2.html#NM2" title="SPPOL_2:NM.2">Special_polygon_in_R2</a>;<br/>

<b>consider </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font> being   <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> 2</span>)</span>, <font color="Maroon" title="c4">P1</font>, <font color="Maroon" title="c5">P2</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> 2</span>)</span><b> such that </b><br/><a NAME="E2:97"/>
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">q</font> &amp; <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> )
 <b>and </b><br/><a NAME="E3:97"/><i><font color="Green" title="E74">A1</font></i>: 
( <font color="Maroon" title="c4">P1</font> <a href="topreal4.html#R1" title="TOPREAL4:pred.1">is_S-P_arc_joining</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font> &amp; <font color="Maroon" title="c5">P2</font> <a href="topreal4.html#R1" title="TOPREAL4:pred.1">is_S-P_arc_joining</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font> )
 <b>and </b><br/><a NAME="E4:97"/>
<font color="Maroon" title="c4">P1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>and </b><br/><a NAME="E5:97"/><i><font color="Green" title="E75">A2</font></i>: 
<font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c5">P2</font>
 <b>by </b><i><a class="ref" href="topreal4.html#D2" title="TOPREAL4:def.2">TOPREAL4:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">P1</font> = <font color="Maroon" title="c4">P1</font>, <font color="Maroon" title="c7">P2</font> = <font color="Maroon" title="c5">P2</font> as   <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> 2</span>)</span> ;<br/>
<a NAME="E7:97"/>
( <font color="Maroon" title="c6">P1</font> <a href="topreal1.html#NR3" title="TOPREAL1:NR.3">is_S-P_arc</a>  &amp; <font color="Maroon" title="c7">P2</font> <a href="topreal1.html#NR3" title="TOPREAL1:NR.3">is_S-P_arc</a>  )
 
<b>by </b><i><a class="txt" href="sppol_2.html#E3:97"><i><font color="Green" title="E74">A1</font></i></a>, <a class="ref" href="topreal4.html#T2" title="TOPREAL4:th.2">TOPREAL4:2</a></i>;<br/>
<a NAME="E8:97"/><b>then </b>
( <font color="Maroon" title="c6">P1</font> is <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a> &amp; <font color="Maroon" title="c7">P2</font> is <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a> )
 
<b>by </b><i><a class="ref" href="sppol_2.html#T62" target="_self" title="SPPOL_2:th.62">Th62</a></i>;<br/>
<b>hence </b><a NAME="E9:97"/>
<font color="Maroon" title="c1">G</font> is <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a>
 <b>by </b><i><a class="txt" href="sppol_2.html#E5:97"><i><font color="Green" title="E75">A2</font></i></a>, <a class="ref" href="compts_1.html#T19" title="COMPTS_1:th.19">COMPTS_1:19</a></i>;<br/>


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