<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">M</font> be   <a href="sub_metr.html#NM1">PseudoMetricSpace</a>;<br/><b>let </b><font color="Maroon">V</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">M</font> <a href="metric_2.html#K2" target="_self">-neighbour</a> , <font color="Maroon">Q</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">M</font> <a href="metric_2.html#K2" target="_self">-neighbour</a> ;<br/>



<b>consider </b><font color="Maroon">p</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">M</font><b> such that </b><br/><a NAME="E2:49"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">V</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="metric_2.html#K1" target="_self">-neighbour</a> 
 <b>by </b><i/>;<br/>
<a NAME="E3:49"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font>
 
<b>by </b><i><a class="ref" href="metric_2.html#D3" target="_self">Def3</a>, </i>;<br/>
<b>consider </b><font color="Maroon">q</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">M</font><b> such that </b><br/><a NAME="E5:49"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">Q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="metric_2.html#K1" target="_self">-neighbour</a> 
 <b>by </b><i/>;<br/>
<a NAME="E6:49"/>
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q</font>
 
<b>by </b><i><a class="txt" href="metric_2.html#E4"><i><font color="Green">Lemma26</font></i></a>, </i>;<br/>
<a NAME="E7:49"/><b>then </b>
<font color="Maroon">V</font>,<font color="Maroon">Q</font> <a href="metric_2.html#R4" target="_self">is_dst</a>  <a href="metric_1.html#K4">dist</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E8:49"/>
 ex <font color="Olive">v</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a>  st <font color="Maroon">V</font>,<font color="Maroon">Q</font> <a href="metric_2.html#R4" target="_self">is_dst</a> <font color="Olive">v</font>
 ;<br/>


</div>
