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

<b>let </b><font color="Maroon">p</font> be   <a href="pre_topc.html#NM2">Point</a> of <a href="metric_1.html#K8">RealSpace</a> , <font color="Maroon">q</font> be   <a href="pre_topc.html#NM2">Point</a> of <a href="metric_1.html#K8">RealSpace</a> ;<br/><b>let </b><font color="Maroon">x</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">y</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>assume </b><a NAME="E1:23"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> )
 ;<br/>

<a NAME="E2:23"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">x</font> is   <a href="real_1.html#NM1">Real</a> &amp; <font color="Maroon">y</font> is   <a href="real_1.html#NM1">Real</a> )
 
<b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/>
<b>thus </b> <a href="metric_1.html#K4">dist</a> <font color="Maroon">p</font>,<font color="Maroon">q</font> = 
<a href="metric_1.html#K7">real_dist</a>  <a href="binop_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>, <a class="ref" href="metric_1.html#D14">METRIC_1:def 14</a></i>
<br/>.= 
 <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i>, <a class="ref" href="metric_1.html#D13">METRIC_1:def 13</a></i>
;<br/>


</div>
