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<b>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="metric_1.html#K8">RealSpace</a> , <font color="Maroon">q</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="metric_1.html#K8">RealSpace</a> ;<br/>

<b>assume </b><a NAME="E1:30"/>
<font color="Maroon">p</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">q</font>
 ;<br/>

<a NAME="E2:30"/><b>then </b><i><font color="Green">E34</font></i>: 
<font color="Maroon">q</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">p</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/>
 <a href="metric_1.html#K4">dist</a> <font color="Maroon">p</font>,<font color="Maroon">q</font> = 
 <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">p</font></span>)</span>
<b>by </b><i><a class="ref" href="topmetr.html#T15">TOPMETR:15</a></i>
<br/>.= 
<font color="Maroon">q</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">p</font>
<b>by </b><i>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
;<br/>
<b>hence </b><a NAME="E4:30"/>
 <a href="metric_1.html#K4">dist</a> <font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">p</font>
 ;<br/>


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