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<b>let </b><font color="Maroon">PM</font> be    <a href="metric_1.html#L1">MetrStruct</a> ;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">PM</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="E1:34"/>
<font color="Maroon">PM</font> is <a href="metric_1.html#V9">triangle</a>
 ;<br/>

<a NAME="E2:34"/><b>then </b>
for <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">PM</font>  st <font color="Olive">y</font> <a href="hidden.html#R2">in</a>  <a href="metric_1.html#K9">Ball</a> <font color="Maroon">x</font>,<font color="Maroon">r</font> holds <br/> ex <font color="Olive">p</font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <font color="Olive">p</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp;  <a href="metric_1.html#K9">Ball</a> <font color="Olive">y</font>,<font color="Olive">p</font> <a href="tarski.html#R1">c=</a>  <a href="metric_1.html#K9">Ball</a> <font color="Maroon">x</font>,<font color="Maroon">r</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:34"/>
 <a href="metric_1.html#K9">Ball</a> <font color="Maroon">x</font>,<font color="Maroon">r</font> <a href="hidden.html#R2">in</a>  <a href="pcomps_1.html#K3" target="_self">Family_open_set</a> <font color="Maroon">PM</font>
 <b>by </b><i/>;<br/>


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