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

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="metric_1.html#G1">MetrStruct</a>(# <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default"><a href="numbers.html#K1">REAL</a> ,<a href="numbers.html#K1">REAL</a> ,<a href="numbers.html#K1">REAL</a> </span><a href="zfmisc_1.html#K3">:]</a></span>,<a href="metric_4.html#K11" target="_self">taxi_dist3</a>  #), <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="metric_1.html#G1">MetrStruct</a>(# <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default"><a href="numbers.html#K1">REAL</a> ,<a href="numbers.html#K1">REAL</a> ,<a href="numbers.html#K1">REAL</a> </span><a href="zfmisc_1.html#K3">:]</a></span>,<a href="metric_4.html#K11" target="_self">taxi_dist3</a>  #), <font color="Maroon">z</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="metric_1.html#G1">MetrStruct</a>(# <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default"><a href="numbers.html#K1">REAL</a> ,<a href="numbers.html#K1">REAL</a> ,<a href="numbers.html#K1">REAL</a> </span><a href="zfmisc_1.html#K3">:]</a></span>,<a href="metric_4.html#K11" target="_self">taxi_dist3</a>  #);<br/><b>reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x</font>, <font color="Maroon">y'</font> = <font color="Maroon">y</font>, <font color="Maroon">z'</font> = <font color="Maroon">z</font> as    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default"><a href="numbers.html#K1">REAL</a> ,<a href="numbers.html#K1">REAL</a> ,<a href="numbers.html#K1">REAL</a> </span><a href="zfmisc_1.html#K3">:]</a></span> ;<br/><a NAME="E2:32_1_1_1"/><i><font color="Green">E27</font></i>: 
 <a href="metric_1.html#K2">dist</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <a href="metric_4.html#K11" target="_self">taxi_dist3</a>  <a href="metric_1.html#K1">.</a> <font color="Maroon">x'</font>,<font color="Maroon">y'</font>
 <b>by </b><i><a class="ref" href="metric_1.html#D1">METRIC_1:def 1</a></i>;<br/><a NAME="E3:32_1_1_1"/><i><font color="Green">E28</font></i>: 
 <a href="metric_1.html#K2">dist</a> <font color="Maroon">x</font>,<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <a href="metric_4.html#K11" target="_self">taxi_dist3</a>  <a href="metric_1.html#K1">.</a> <font color="Maroon">x'</font>,<font color="Maroon">z'</font>
 <b>by </b><i><a class="ref" href="metric_1.html#D1">METRIC_1:def 1</a></i>;<br/><a NAME="E4:32_1_1_1"/><i><font color="Green">E31</font></i>: 
 <a href="metric_1.html#K2">dist</a> <font color="Maroon">y</font>,<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <a href="metric_4.html#K11" target="_self">taxi_dist3</a>  <a href="metric_1.html#K1">.</a> <font color="Maroon">y'</font>,<font color="Maroon">z'</font>
 <b>by </b><i><a class="ref" href="metric_1.html#D1">METRIC_1:def 1</a></i>;<br/><a NAME="E5:32_1_1_1"/><i><font color="Green">E32</font></i>: 
 <a href="metric_1.html#K2">dist</a> <font color="Maroon">y</font>,<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <a href="metric_4.html#K11" target="_self">taxi_dist3</a>  <a href="metric_1.html#K1">.</a> <font color="Maroon">y'</font>,<font color="Maroon">x'</font>
 <b>by </b><i><a class="ref" href="metric_1.html#D1">METRIC_1:def 1</a></i>;<br/><b>thus </b><a NAME="E6:32_1_1_1"/>
(  <a href="metric_1.html#K2">dist</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> 0 iff <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i>, </i>;<br/><b>thus </b><a NAME="E7:32_1_1_1"/>
 <a href="metric_1.html#K2">dist</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="metric_1.html#K2">dist</a> <font color="Maroon">y</font>,<font color="Maroon">x</font>
 <b>by </b><i>, , </i>;<br/><b>thus </b><a NAME="E8:32_1_1_1"/>
 <a href="metric_1.html#K2">dist</a> <font color="Maroon">x</font>,<font color="Maroon">z</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="metric_1.html#K2">dist</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="metric_1.html#K2">dist</a> <font color="Maroon">y</font>,<font color="Maroon">z</font></span>)</span>
 <b>by </b><i>, <a class="txt" href="metric_4.html#E2:32_1_1_1"><i><font color="Green">E27</font></i></a>, <a class="txt" href="metric_4.html#E3:32_1_1_1"><i><font color="Green">E28</font></i></a>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:32_1_1"/>
 <a href="metric_1.html#G1">MetrStruct</a>(# <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default"><a href="numbers.html#K1">REAL</a> ,<a href="numbers.html#K1">REAL</a> ,<a href="numbers.html#K1">REAL</a> </span><a href="zfmisc_1.html#K3">:]</a></span>,<a href="metric_4.html#K11" target="_self">taxi_dist3</a>  #) is  non <a href="struct_0.html#V3">empty</a> <a href="metric_1.html#V1">strict</a> <a href="metric_1.html#NM1">MetrSpace</a>
 <b>by </b><i><a class="ref" href="metric_1.html#T6">METRIC_1:6</a></i>;<br/>


</div>
