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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">M</font> <a href="metric_2.html#K2" target="_self">-neighbour</a> ,   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">M</font> <a href="metric_2.html#K2" target="_self">-neighbour</a> ,   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a> ] <b>means </b><font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">a<sub>2</sub></font> <a href="metric_2.html#R4" target="_self">is_dst</a> <font color="Maroon">a<sub>3</sub></font>;<br/>
<a NAME="E1:50_1_1"/><i><font color="Green">E28</font></i>: 
for <font color="Olive">V</font>, <font color="Olive">Q</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">M</font> <a href="metric_2.html#K2" target="_self">-neighbour</a>   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">S<sub>1</sub></font>[<font color="Olive">V</font>,<font color="Olive">Q</font>,<font color="Olive">v</font>]
 
<b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">F</font> being   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="metric_2.html#K2" target="_self">-neighbour</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="metric_2.html#K2" target="_self">-neighbour</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>, <a href="numbers.html#K1">REAL</a> <b> such that </b><br/><a NAME="E3:50_1_1"/><i><font color="Green">E29</font></i>: 
for <font color="Olive">V</font>, <font color="Olive">Q</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">M</font> <a href="metric_2.html#K2" target="_self">-neighbour</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">V</font>,<font color="Olive">Q</font>,<font color="Maroon">F</font> <a href="metric_1.html#K1">.</a> <font color="Olive">V</font>,<font color="Olive">Q</font>]
 <b>from </b><i><a class="ref" href="binop_1.html#S3">BINOP_1:sch 3</a>(<a class="ref" href="metric_2.html#D3" target="_self">Def3</a>);<br/></i>
<b>take </b>
<font color="Maroon">F</font>
;<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>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">M</font>, <font color="Maroon">q</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">M</font>;<br/>



<b>assume </b><a NAME="E4:50_1_1"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font> &amp; <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q</font> )
 ;<br/>

<a NAME="E5:50_1_1"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">V</font>,<font color="Maroon">Q</font> <a href="metric_2.html#R4" target="_self">is_dst</a> <font color="Maroon">F</font> <a href="metric_1.html#K1">.</a> <font color="Maroon">V</font>,<font color="Maroon">Q</font>
 
<b>by </b><i/>;<br/>
<b>thus </b><a NAME="E6:50_1_1"/>
<font color="Maroon">F</font> <a href="metric_1.html#K1">.</a> <font color="Maroon">V</font>,<font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="metric_1.html#K4">dist</a> <font color="Maroon">p</font>,<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>, <a class="ref" href="metric_2.html#T6" target="_self">Th6</a>, </i>;<br/>


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