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<a NAME="E1:7_1_1"/>
( the <a href="metric_1.html#U1">distance</a> of <a href="metric_1.html#G1">MetrStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>,<span class="p1">(<span class="default"><a href="normsp_2.html#K1" target="_self">distance_by_norm_of</a> <font color="Maroon">X</font></span>)</span> #) is <a href="metric_1.html#V2">Reflexive</a> &amp; the <a href="metric_1.html#U1">distance</a> of <a href="metric_1.html#G1">MetrStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>,<span class="p1">(<span class="default"><a href="normsp_2.html#K1" target="_self">distance_by_norm_of</a> <font color="Maroon">X</font></span>)</span> #) is <a href="metric_1.html#V3">discerning</a> &amp; the <a href="metric_1.html#U1">distance</a> of <a href="metric_1.html#G1">MetrStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>,<span class="p1">(<span class="default"><a href="normsp_2.html#K1" target="_self">distance_by_norm_of</a> <font color="Maroon">X</font></span>)</span> #) is <a href="metric_1.html#V4">symmetric</a> &amp; the <a href="metric_1.html#U1">distance</a> of <a href="metric_1.html#G1">MetrStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>,<span class="p1">(<span class="default"><a href="normsp_2.html#K1" target="_self">distance_by_norm_of</a> <font color="Maroon">X</font></span>)</span> #) is <a href="metric_1.html#V5">triangle</a> )
 
<b>by </b><i>, , , </i>;<br/>
<b>hence </b><a NAME="E2:7_1_1"/>
 <a href="metric_1.html#G1">MetrStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>,<span class="p1">(<span class="default"><a href="normsp_2.html#K1" target="_self">distance_by_norm_of</a> <font color="Maroon">X</font></span>)</span> #) is  non <a href="struct_0.html#V3">empty</a> <a href="metric_1.html#NM1">MetrSpace</a>
 <b>by </b><i><a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a>, <a class="ref" href="metric_1.html#D7">METRIC_1:def 7</a>, <a class="ref" href="metric_1.html#D8">METRIC_1:def 8</a>, <a class="ref" href="metric_1.html#D9">METRIC_1:def 9</a>, <a class="ref" href="metric_1.html#D10">METRIC_1:def 10</a></i>;<br/>


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