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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">A</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="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>, <font color="Maroon">B</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="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>;<br/>



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 ex <font color="Olive">A'</font>, <font color="Olive">B'</font> being  <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="pcomps_1.html#K4">TopSpaceMetr</a> <span class="p2">(<span class="default"><a href="euclid.html#K14">Euclid</a> <font color="Maroon">n</font></span>)</span></span>)</span> st <br/>( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Olive">A'</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Olive">B'</font> &amp;  <a href="jordan1k.html#K1" target="_self">dist_min</a> <font color="Maroon">A</font>,<font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="weierstr.html#K9">min_dist_min</a> <font color="Olive">A'</font>,<font color="Olive">B'</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:41"/>
 <a href="jordan1k.html#K1" target="_self">dist_min</a> <font color="Maroon">A</font>,<font color="Maroon">B</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i/>;<br/>


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