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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="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">x</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> <font color="Maroon">n</font></span>)</span>;<br/>





<b>reconsider </b><font color="Maroon">e</font> = <font color="Maroon">x</font> as   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14">Euclid</a> <font color="Maroon">n</font></span>)</span> <b>by </b><i><a class="ref" href="topreal3.html#T13">TOPREAL3:13</a></i>;<br/>
<a NAME="E2:18"/><i><font color="Green">E42</font></i>: 
 <a href="topreal9.html#K3" target="_self">Sphere</a> <font color="Maroon">x</font>,<font color="Maroon">r</font> <a href="hidden.html#R1">=</a>  <a href="metric_1.html#K11">Sphere</a> <font color="Maroon">e</font>,<font color="Maroon">r</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:18"/>
 <a href="topreal9.html#K2" target="_self">cl_Ball</a> <font color="Maroon">x</font>,<font color="Maroon">r</font> <a href="hidden.html#R1">=</a>  <a href="metric_1.html#K10">cl_Ball</a> <font color="Maroon">e</font>,<font color="Maroon">r</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:18"/>
 <a href="topreal9.html#K3" target="_self">Sphere</a> <font color="Maroon">x</font>,<font color="Maroon">r</font> <a href="tarski.html#R1">c=</a>  <a href="topreal9.html#K2" target="_self">cl_Ball</a> <font color="Maroon">x</font>,<font color="Maroon">r</font>
 <b>by </b><i>, <a class="ref" href="metric_1.html#T16">METRIC_1:16</a></i>;<br/>


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