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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">r</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="complsp1.html#K8" target="_self">COMPLEX</a> <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="complsp1.html#K8" target="_self">COMPLEX</a> <font color="Maroon">n</font></span>)</span>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:93"/><i><font color="Green">E59</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">r</font>
 <b>and </b><br/><a NAME="E2:93"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E3:93"/>
 <a href="complsp1.html#K18" target="_self">dist</a> <font color="Maroon">x</font>,<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="complsp1.html#T43" target="_self">Th43</a>, <a class="ref" href="complsp1.html#T32" target="_self">Th32</a></i>;<br/>
<a NAME="E4:93"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">z</font> where <font color="Olive">z</font> is    <a href="finseq_2.html#M2">Element</a> of  <a href="complsp1.html#K8" target="_self">COMPLEX</a> <font color="Maroon">n</font> :  <a href="complsp1.html#K18" target="_self">dist</a> <font color="Olive">z</font>,<font color="Maroon">A</font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">r</font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="complsp1.html#T42" target="_self">Th42</a></i>;<br/>
<b>hence </b><a NAME="E5:93"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="complsp1.html#K19" target="_self">Ball</a> <font color="Maroon">A</font>,<font color="Maroon">r</font>
 ;<br/>


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