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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">A</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> <font color="Maroon">n</font></span>)</span>;<br/><b>let </b><font color="Maroon">B</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> <font color="Maroon">n</font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:31"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">B</font> <a href="jordan2c.html#R2" target="_self">is_outside_component_of</a> <font color="Maroon">A</font>
 ;<br/>

<b>let </b><font color="Maroon">x</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="E2:31"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 ;<br/>

<a NAME="E3:31"/>
<font color="Maroon">B</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">B2</font> where <font color="Olive">B2</font> is   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span> : <font color="Olive">B2</font> <a href="jordan2c.html#R2" target="_self">is_outside_component_of</a> <font color="Maroon">A</font> </span>}</span> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:31"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="jordan2c.html#K2" target="_self">UBD</a> <font color="Maroon">A</font>
 <b>by </b><i>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>


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