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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="metric_1.html#NM1">MetrSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="pcomps_1.html#K4">TopSpaceMetr</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>



<i><font color="Green">E28</font></i>:  <a href="weierstr.html#K3">[#]</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="weierstr.html#K8">dist_min</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="weierstr.html#K8">dist_min</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="weierstr.html#D3">WEIERSTR:def 3</a></i>
<br/>.= 
<span class="p1"><a href="seq_4.html#K1">{</a><span class="default">0</span><a href="seq_4.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="hausdorf.html#T29" target="_self">Th29</a></i>
;<br/>
 <a href="weierstr.html#K10">max_dist_min</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font> = 
 <a href="weierstr.html#K4">upper_bound</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="weierstr.html#K8">dist_min</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="weierstr.html#D10">WEIERSTR:def 10</a></i>
<br/>.= 
 <a href="seq_4.html#K4">upper_bound</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default">0</span><a href="seq_4.html#K1">}</a></span>
<b>by </b><i><a class="txt" href="hausdorf.html#E1:33"><i><font color="Green">E28</font></i></a>, <a class="ref" href="weierstr.html#D4">WEIERSTR:def 4</a></i>
;<br/>
<b>hence </b><a NAME="E3:33"/>
 <a href="weierstr.html#K10">max_dist_min</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="seq_4.html#T22">SEQ_4:22</a></i>;<br/>


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