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<b>let </b><font color="Maroon">N</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="metric_1.html#L1">MetrStruct</a> ;<br/><b>let </b><font color="Maroon">w</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font>;<br/><b>let </b><font color="Maroon">r</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="E1:24"/>
<font color="Maroon">N</font> is <a href="metric_1.html#V6">Reflexive</a>
 ;<br/>

<a NAME="E2:24"/><b>then </b><i><font color="Green">E44</font></i>: 
 <a href="metric_1.html#K2">dist</a> <font color="Maroon">w</font>,<font color="Maroon">w</font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="metric_1.html#T1">METRIC_1:1</a></i>;<br/>
<b>assume </b><a NAME="E3:24"/>
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">r</font>
 ;<br/>

<b>hence </b><a NAME="E4:24"/>
<font color="Maroon">w</font> <a href="hidden.html#R2">in</a>  <a href="metric_1.html#K9">Ball</a> <font color="Maroon">w</font>,<font color="Maroon">r</font>
 <b>by </b><i>, <a class="ref" href="metric_1.html#T12">METRIC_1:12</a></i>;<br/>


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