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<b>let </b><font color="Maroon">M</font> be   <a href="metric_1.html#NM1">MetrSpace</a>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">M</font>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">M</font>;<br/>



<b>assume </b><a NAME="E1:2"/>
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font>
 ;<br/>

<a NAME="E2:2"/><b>then </b>
 <a href="metric_1.html#K4">dist</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="metric_1.html#T2">METRIC_1:2</a></i>;<br/>
<b>hence </b><a NAME="E3:2"/>
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="metric_1.html#K4">dist</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="metric_1.html#T5">METRIC_1:5</a></i>;<br/>


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