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<b>let </b><font color="Maroon">M</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">P</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">M</font></span>)</span>;<br/><b>let </b><font color="Maroon">z</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">M</font>;<br/>





<b>consider </b><font color="Maroon">w</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:20"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">w</font> = <font color="Maroon">w</font> as   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">M</font> <b>by </b><i>, <a class="ref" href="topmetr.html#T16">TOPMETR:16</a></i>;<br/>
<b>take </b>
<font color="Maroon">w</font>
;<br/>

<b>thus </b><a NAME="E4:20"/>
<font color="Maroon">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font>
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E5:20"/>
<span class="p1">(<span class="default"><a href="weierstr.html#K8">dist_min</a> <font color="Maroon">P</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="metric_1.html#K4">dist</a> <font color="Maroon">w</font>,<font color="Maroon">z</font>
 <b>by </b><i>, </i>;<br/>


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