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

<span class="kw">let </span><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <a href="metric_3.html#K20" title="METRIC_3:func.20">taxi_dist3</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  iff <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c3">x1</font> = <font color="Maroon" title="c1">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> , <font color="Maroon" title="c4">x2</font> = <font color="Maroon" title="c1">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> , <font color="Maroon" title="c5">x3</font> = <font color="Maroon" title="c1">x</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a> , <font color="Maroon" title="c6">y1</font> = <font color="Maroon" title="c2">y</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> , <font color="Maroon" title="c7">y2</font> = <font color="Maroon" title="c2">y</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> , <font color="Maroon" title="c8">y3</font> = <font color="Maroon" title="c2">y</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  ;<br/>
<a NAME="E2:50"/><span class="lab"><font color="Green" title="E36">A1</font></span>: 
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">x3</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c6">y1</font>,<font color="Maroon" title="c7">y2</font>,<font color="Maroon" title="c8">y3</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T44" title="MCART_1:th.44">MCART_1:44</a></span>;<br/>
<span class="kw">thus </span><a NAME="E3:50"/>
( <a href="metric_3.html#K20" title="METRIC_3:func.20">taxi_dist3</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> implies <a href="metric_3.html#K20" title="METRIC_3:func.20">taxi_dist3</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">set </span><font color="Maroon" title="c9">d3</font> = <a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c5">x3</font>,<font color="Maroon" title="c8">y3</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c10">d2</font> = <a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c7">y2</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c11">d1</font> = <a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c6">y1</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c12">d4</font> = <span class="p1">(<span class="default"><a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c6">y1</font>)</span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c7">y2</font>)</span>)</span>;<br/>
<a NAME="E1:50_1"/>
<a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c5">x3</font>,<font color="Maroon" title="c8">y3</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x3</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c8">y3</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="metric_1.html#D12" title="METRIC_1:def.12">METRIC_1:def 12</a></span>;<br/>
<a NAME="E2:50_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A2</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c5">x3</font>,<font color="Maroon" title="c8">y3</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T46" title="COMPLEX1:th.46">COMPLEX1:46</a></span>;<br/>
<a NAME="E3:50_1"/>
<a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c6">y1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c6">y1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="metric_1.html#D12" title="METRIC_1:def.12">METRIC_1:def 12</a></span>;<br/>
<a NAME="E4:50_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A3</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c6">y1</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T46" title="COMPLEX1:th.46">COMPLEX1:46</a></span>;<br/>
<span class="kw">assume </span><a NAME="E5:50_1"/>
<a href="metric_3.html#K20" title="METRIC_3:func.20">taxi_dist3</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font></span><br/>

<a NAME="E6:50_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A4</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c6">y1</font>)</span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c7">y2</font>)</span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c5">x3</font>,<font color="Maroon" title="c8">y3</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:50"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="ref" href="metric_3.html#D20" target="_self" title="METRIC_3:def.20">Def20</a></span>;<br/>
<a NAME="E7:50_1"/>
<a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c7">y2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x2</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c7">y2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="metric_1.html#D12" title="METRIC_1:def.12">METRIC_1:def 12</a></span>;<br/>
<a NAME="E8:50_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A5</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c7">y2</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T46" title="COMPLEX1:th.46">COMPLEX1:46</a></span>;<br/>
<a NAME="E9:50_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A6</font></span>: 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c6">y1</font>)</span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c7">y2</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:50_1"><span class="lab"><font color="Green" title="E38">A3</font></span></a>, <a class="ref" href="xreal_1.html#T7" title="XREAL_1:th.7">XREAL_1:7</a></span>;<br/>
<a NAME="E10:50_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A7</font></span>: 
<span class="p1">(<span class="default"><a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c6">y1</font>)</span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c7">y2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:50_1"><span class="lab"><font color="Green" title="E39">A4</font></span></a>, <a class="txt" href="#E2:50_1"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <a class="ref" href="xreal_1.html#T27" title="XREAL_1:th.27">XREAL_1:27</a></span>;<br/>
<a NAME="E11:50_1"/><span class="kw">then </span>
<a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c6">y1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:50_1"><span class="lab"><font color="Green" title="E40">A5</font></span></a>, <a class="txt" href="#E4:50_1"><span class="lab"><font color="Green" title="E38">A3</font></span></a>, <a class="ref" href="xreal_1.html#T27" title="XREAL_1:th.27">XREAL_1:27</a></span>;<br/>
<a NAME="E12:50_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A8</font></span>: 
<font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="metric_1.html#T8" title="METRIC_1:th.8">METRIC_1:8</a></span>;<br/>
<a NAME="E13:50_1"/>
<a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c5">x3</font>,<font color="Maroon" title="c8">y3</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:50_1"><span class="lab"><font color="Green" title="E39">A4</font></span></a>, <a class="txt" href="#E2:50_1"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <a class="txt" href="#E9:50_1"><span class="lab"><font color="Green" title="E41">A6</font></span></a>, <a class="ref" href="xreal_1.html#T27" title="XREAL_1:th.27">XREAL_1:27</a></span>;<br/>
<a NAME="E14:50_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A9</font></span>: 
<font color="Maroon" title="c5">x3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">y3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="metric_1.html#T8" title="METRIC_1:th.8">METRIC_1:8</a></span>;<br/>
<a NAME="E15:50_1"/>
<a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c7">y2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:50_1"><span class="lab"><font color="Green" title="E40">A5</font></span></a>, <a class="txt" href="#E4:50_1"><span class="lab"><font color="Green" title="E38">A3</font></span></a>, <a class="txt" href="#E10:50_1"><span class="lab"><font color="Green" title="E42">A7</font></span></a>, <a class="ref" href="xreal_1.html#T27" title="XREAL_1:th.27">XREAL_1:27</a></span>;<br/>
<span class="kw">hence </span><a NAME="E16:50_1"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:50"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="txt" href="#E14:50_1"><span class="lab"><font color="Green" title="E44">A9</font></span></a>, <a class="txt" href="#E12:50_1"><span class="lab"><font color="Green" title="E43">A8</font></span></a>, <a class="ref" href="metric_1.html#T8" title="METRIC_1:th.8">METRIC_1:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E4:50"/><span class="lab"><font color="Green" title="E37">A10</font></span>: 
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <a href="metric_3.html#K20" title="METRIC_3:func.20">taxi_dist3</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><br/>

<a NAME="E5:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A11</font></span>: 
( <a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c6">y1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c7">y2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="metric_1.html#T8" title="METRIC_1:th.8">METRIC_1:8</a></span>;<br/>
<a href="metric_3.html#K20" title="METRIC_3:func.20">taxi_dist3</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c6">y1</font>)</span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c7">y2</font>)</span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="metric_1.html#K7" title="METRIC_1:func.7">real_dist</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c5">x3</font>,<font color="Maroon" title="c8">y3</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:50"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="ref" href="metric_3.html#D20" target="_self" title="METRIC_3:def.20">Def20</a></span>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:50"><span class="lab"><font color="Green" title="E37">A10</font></span></a>, <a class="txt" href="#E5:50"><span class="lab"><font color="Green" title="E38">A11</font></span></a>, <a class="ref" href="metric_1.html#T8" title="METRIC_1:th.8">METRIC_1:8</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E7:50"/>
<a href="metric_3.html#K20" title="METRIC_3:func.20">taxi_dist3</a> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> (<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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