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<b>let </b><font color="Maroon">C</font> be   <a href="topreal2.html#NM1">Simple_closed_curve</a>;<br/><b>let </b><font color="Maroon">A1</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> 2</span>)</span>, <font color="Maroon">A2</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> 2</span>)</span>;<br/><b>let </b><font color="Maroon">p1</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> 2</span>)</span>, <font color="Maroon">p2</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> 2</span>)</span>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:16"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">A1</font> <a href="topreal1.html#R1">is_an_arc_of</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>
 <b>and </b><br/><a NAME="E2:16"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">A2</font> <a href="topreal1.html#R1">is_an_arc_of</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>
 <b>and </b><br/><a NAME="E3:16"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">A1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font>
 <b>and </b><br/><a NAME="E4:16"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">A2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font>
 <b>and </b><br/><a NAME="E5:16"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">A1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">p1</font>,<font color="Maroon">p2</font></span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<a NAME="E6:16"/>
<font color="Maroon">A1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">A2</font>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E7:16"/>
<font color="Maroon">A1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">A2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 <b>by </b><i>, , , , </i>;<br/>


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