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<b>let </b><font color="Maroon">C</font> be   <a href="topreal2.html#NM1">Simple_closed_curve</a>;<br/>

<a NAME="E1:156"/>
<font color="Maroon">C</font> is <a href="jordan1.html#V2">Jordan</a>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:156"/>
 ex <font color="Olive">A1</font>, <font color="Olive">A2</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> st <br/>( <font color="Maroon">C</font> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a> <font color="Olive">A1</font> <a href="subset_1.html#K4">\/</a> <font color="Olive">A2</font> &amp; <font color="Olive">A1</font> <a href="xboole_0.html#R1">misses</a> <font color="Olive">A2</font> &amp; <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Olive">A1</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Olive">A1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Olive">A2</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Olive">A2</font> &amp; ( for <font color="Olive">C1</font>, <font color="Olive">C2</font> being  <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span>  st <font color="Olive">C1</font> <a href="hidden.html#R1">=</a> <font color="Olive">A1</font> &amp; <font color="Olive">C2</font> <a href="hidden.html#R1">=</a> <font color="Olive">A2</font> holds <br/>( <font color="Olive">C1</font> <a href="connsp_1.html#R3">is_a_component_of</a> <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="subset_1.html#K3">`</a> </span>)</span> &amp; <font color="Olive">C2</font> <a href="connsp_1.html#R3">is_a_component_of</a> <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="subset_1.html#K3">`</a> </span>)</span> ) ) )
 <b>by </b><i><a class="ref" href="jordan1.html#D2">JORDAN1:def 2</a></i>;<br/>


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