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<b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>8</sub></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">c<sub>7</sub></font></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>9</sub></font> be  non <a href="xboole_0.html#V1">zero</a> <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>





<b>set </b><font color="Maroon">c<sub>10</sub></font> =  <a href="topreal9.html#K1">Ball</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>;<br/>
<b>thus </b> <a href="tops_1.html#K2">Fr</a> <span class="p1">(<span class="default"><a href="topreal9.html#K1">Ball</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><a href="topreal9.html#K1">Ball</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="topreal9.html#K1">Ball</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="tops_1.html#T76">TOPS_1:76</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="topreal9.html#K2">cl_Ball</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="topreal9.html#K1">Ball</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="jordan.html#T23" target="_self">Th23</a></i>
<br/>.= 
 <a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="ref" href="jordan.html#T19" target="_self">Th19</a></i>
;<br/>


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