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

<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="metric_1.html#V1" title="METRIC_1:attr.1">strict</a> <a href="metric_1.html#NM1" title="METRIC_1:NM.1">MetrSpace</a>;<br/>

<a NAME="E1:4"/><i><font color="Green" title="E4">A1</font></i>: 
the <a href="metric_1.html#U1" title="METRIC_1:sel.1">distance</a> of <font color="Maroon" title="c1">X</font> <a href="pcomps_1.html#R1" title="PCOMPS_1:pred.1">is_metric_of</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="pcomps_1.html#T39" title="PCOMPS_1:th.39">PCOMPS_1:39</a></i>;<br/>
<b>hence </b><a NAME="E2:4"/>
the <a href="metric_1.html#U1" title="METRIC_1:sel.1">distance</a> of <font color="Maroon" title="c1">X</font> is <a href="metric_1.html#V2" title="METRIC_1:attr.2">Reflexive</a>
 <b>by </b><i><a class="ref" href="metric_6.html#T3" target="_self" title="METRIC_6:th.3">Th3</a></i>;<br/>

<b>thus </b><a NAME="E3:4"/>
the <a href="metric_1.html#U1" title="METRIC_1:sel.1">distance</a> of <font color="Maroon" title="c1">X</font> is <a href="metric_1.html#V3" title="METRIC_1:attr.3">discerning</a>
 <b>by </b><i><a class="txt" href="metric_6.html#E1:4"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="metric_6.html#T3" target="_self" title="METRIC_6:th.3">Th3</a></i>;<br/>

<b>thus </b><a NAME="E4:4"/>
the <a href="metric_1.html#U1" title="METRIC_1:sel.1">distance</a> of <font color="Maroon" title="c1">X</font> is <a href="metric_1.html#V4" title="METRIC_1:attr.4">symmetric</a>
 <b>by </b><i><a class="txt" href="metric_6.html#E1:4"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="metric_6.html#T3" target="_self" title="METRIC_6:th.3">Th3</a></i>;<br/>

<b>thus </b><a NAME="E5:4"/>
the <a href="metric_1.html#U1" title="METRIC_1:sel.1">distance</a> of <font color="Maroon" title="c1">X</font> is <a href="metric_1.html#V5" title="METRIC_1:attr.5">triangle</a>
 <b>by </b><i><a class="txt" href="metric_6.html#E1:4"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="metric_6.html#T3" target="_self" title="METRIC_6:th.3">Th3</a></i>;<br/>


</div>
